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Equation Problems (Geometry)
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Question 1 of 9
1. Question
Find `x`
- `x=` (11)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Notice that the full angle has a square marker, which means it is a right angle and measures `90°`.Form an equation knowing that the two smaller angles are complementary and add up to `90°`.
Right Angle`=90°`Small Angle `1=4x°`Small Angle `2=46°`Small Angle `1` `+`Small Angle `2` `=` Right Angle `4x` `+``46` `=` `90` Substitute the values To solve for `x`, it needs to be alone on one side.Start by moving `46` to the other side by subtracting `46` from both sides of the equation.`4``x` `+46` `=` `90` `4``x` `+46` `-46` `=` `90` `-46` `4``x` `=` `44` `46-46` cancels out Finally, remove `4` by dividing both sides of the equation by `4`.`4``x` `=` `44` `4``x``divide4` `=` `44``divide4` `x` `=` `11` `4divide4` cancels out Check our workTo confirm our answer, substitute `x=11` to the formed equation.`4x+46` `=` `90` `4(11)+46` `=` `90` Substitute `x=11` `44+46` `=` `90` `90` `=` `90` Since the equation is true, the answer is correct.`x=11`Hint
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Question 2 of 9
2. Question
Find `x`
- `x=` (16)
Correct
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.A straight angle measures `180°`.Form an equation knowing that the two smaller angles are supplementary and add up to `180°`.
Straight Angle`=180°`Small Angle `1=148°`Small Angle `2=2x°`Small Angle `1` `+`Small Angle `2` `=` Straight Angle `148` `+``2x` `=` `180` Substitute the values `2x+148` `=` `180` To solve for `x`, it needs to be alone on one side.Start by moving `148` to the other side by subtracting `148` from both sides of the equation.`2``x` `+148` `=` `180` `2``x` `+148` `-148` `=` `180` `-148` `2``x` `=` `32` `148-148` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`2``x` `=` `32` `2``x``divide2` `=` `32``divide2` `x` `=` `16` `2divide2` cancels out Check our workTo confirm our answer, substitute `x=16` to the formed equation.`2x+148` `=` `180` `2(16)+148` `=` `180` Substitute `x=16` `32+148` `=` `180` `180` `=` `180` Since the equation is true, the answer is correct.`x=16`Hint
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Question 3 of 9
3. Question
Find `x`
- `x=` (28)
Correct
Well Done!
Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.A straight angle measures `180°`.Form an equation knowing that the three angles are supplementary and add up to `180°`.
Straight Angle`=180°`Angle `1=50°`Angle `2=3x°`Angle `3=(2x-10)°`Angle `1` `+`Angle `2` `+`Angle `3` `=` Straight Angle `50` `+``3x` `+``(2x-10)` `=` `180` Substitute the values `5x+40` `=` `180` Simplify To solve for `x`, it needs to be alone on one side.Start by moving `40` to the other side by subtracting `40` from both sides of the equation.`5``x` `+40` `=` `180` `5``x` `+40` `-40` `=` `180` `-40` `5``x` `=` `140` `40-40` cancels out Finally, remove `5` by dividing both sides of the equation by `5`.`5``x` `=` `140` `5``x``divide5` `=` `140``divide5` `x` `=` `28` `5divide5` cancels out Check our workTo confirm our answer, substitute `x=28` to the formed equation.`50+3x+(2x-10)` `=` `180` `50+3(28)+(2(28)-10)` `=` `180` Substitute `x=28` `50+84+(56-10)` `=` `180` `50+84+46` `=` `180` `180` `=` `180` Since the equation is true, the answer is correct.`x=28`Hint
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Question 4 of 9
4. Question
Find `x`
- `x=` (80)
Correct
Fantastic!
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Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Vertically Opposite Angles
Alternate Angles
Corresponding Angles
Form an equation knowing that vertically opposite angles are equal.
`2x-30` `=` `x+50` To solve for `x`, it needs to be alone on one side.Start by moving `x` to the other side by subtracting `x` from both sides of the equation.`2``x` `-30` `=` `x` `+50` `2``x` `-30` `-x` `=` `x` `+50` `-x` `x` `-30` `=` `50` `x-x` cancels out Finally, move `30` to the other side by adding `30` to both sides of the equation.`x` `-30` `=` `50` `x` `-30` `+30` `=` `50` `+30` `x` `=` `80` `-30+30` cancels out Check our workTo confirm our answer, substitute `x=80` to the formed equation.`2x-30` `=` `x+50` `2(80)-30` `=` `80+50` Substitute `x=80` `160-30` `=` `130` `130` `=` `130` Since the equation is true, the answer is correct.`x=80`Hint
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Question 5 of 9
5. Question
Find `x`
- `x=` (64)
Correct
Excellent!
Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.A revolution measures `360°`.Form an equation knowing that the three angles form a revolution.
Revolution`=360°`Angle `1=x°`Angle `2=3x°`Angle `3=(x+40)°`Angle `1` `+`Angle `2` `+`Angle `3` `=` Revolution `x` `+``3x` `+``(x+40)` `=` `360` Substitute the values `5x+40` `=` `360` Simplify To solve for `x`, it needs to be alone on one side.Start by moving `40` to the other side by subtracting `40` from both sides of the equation.`5``x` `+40` `=` `360` `5``x` `+40` `-40` `=` `360` `-40` `5``x` `=` `320` `40-40` cancels out Finally, remove `5` by dividing both sides of the equation by `5`.`5``x` `=` `320` `5``x``divide5` `=` `320``divide5` `x` `=` `64` `5divide5` cancels out Check our workTo confirm our answer, substitute `x=64` to the formed equation.`x+3x+(x+40)` `=` `360` `64+3(64)+(64+40)` `=` `360` Substitute `x=64` `64+192+104` `=` `360` `360` `=` `360` Since the equation is true, the answer is correct.`x=64`Hint
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Question 6 of 9
6. Question
Find `y`
- `y=` (25)
Correct
Good Job!
Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Vertically Opposite Angles
Alternate Angles
Corresponding Angles
Form an equation knowing that alternate angles are equal.
`3y+15` `=` `2y+40` To solve for `y`, it needs to be alone on one side.Start by moving `2y` to the other side by subtracting `2y` from both sides of the equation.`3``y` `+15` `=` `2``y` `+40` `3``y` `+15` `-2y` `=` `2``y` `+40` `-2y` `y` `+15` `=` `40` `2y-2y` cancels out Finally, move `15` to the other side by subtracting `15` from both sides of the equation.`y` `+15` `=` `40` `y` `+15` `-15` `=` `40` `-15` `y` `=` `25` `15-15` cancels out Check our workTo confirm our answer, substitute `y=25` to the formed equation.`3y+15` `=` `2y+40` `3(25)+15` `=` `2(25)+40` Substitute `y=25` `75+15` `=` `50+40` `90` `=` `90` Since the equation is true, the answer is correct.`y=25`Hint
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Question 7 of 9
7. Question
Find `y`
- `y=` (4)
Correct
Fantastic!
Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Vertically Opposite Angles
Alternate Angles
Corresponding Angles
Form an equation knowing that corresponding angles are equal.
`7y-27` `=` `5y-19` To solve for `y`, it needs to be alone on one side.Start by moving `5y` to the other side by subtracting `5y` from both sides of the equation.`7``y` `-27` `=` `5``y` `-19` `7``y` `-27` `-5y` `=` `5``y` `-19` `-5y` `2``y` `-27` `=` `-19` `5y-5y` cancels out Next, move `27` to the other side by adding `27` to both sides of the equation.`2``y` `-27` `=` `-19` `2``y` `-27` `+27` `=` `-19` `+27` `2``y` `=` `8` `-27+27` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`2``y` `=` `8` `2``y``divide2` `=` `8``divide2` `y` `=` `4` `2divide2` cancels out Check our workTo confirm our answer, substitute `y=4` to the formed equation.`7y-27` `=` `5y-19` `7(4)-27` `=` `5(4)-19` Substitute `y=4` `28-27` `=` `20-19` `1` `=` `1` Since the equation is true, the answer is correct.`y=4`Hint
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Question 8 of 9
8. Question
Find `y`
- `y=` (40)
Correct
Excellent!
Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Form an equation knowing that the sum of all interior angles of a triangle is `180°`.
Sum of Interior Angles`=180°`Angle `1=70°`Angle `2=(2y-10)°`Angle `3=y°`Angle `1` `+`Angle `2` `+`Angle `3` `=` Sum of Interior Angles `70°` `+``(2y-10)°` `+``y°` `=` `180` Substitute the values `3y+60` `=` `180` To solve for `y`, it needs to be alone on one side.Start by moving `60` to the other side by subtracting `60` from both sides of the equation.`3``y` `+60` `=` `180` `3``y` `+60` `-60` `=` `180` `-60` `3``y` `=` `120` `60-60` cancels out Finally, remove `3` by dividing both sides of the equation by `3`.`3``y` `=` `120` `3``y``divide3` `=` `120``divide3` `y` `=` `40` `3divide3` cancels out Check our workTo confirm our answer, substitute `y=40` to the formed equation.`70+(2y-10)+y` `=` `180` `70+(2(40)-10)+40` `=` `180` Substitute `y=40` `70+(80-10)+40` `=` `180` `70+70+40` `=` `180` `180` `=` `180` Since the equation is true, the answer is correct.`y=40`Hint
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Question 9 of 9
9. Question
Find `x`
- `x=` (36)
Correct
Great Work!
Incorrect
Help VideoInverse Operations
When moving a term to the other side of an equation, the operation is inversed.Form an equation knowing that the sum of all interior angles of a quadrilateral is `360°`.
Sum of Interior Angles`=360°`Angle `1=x°`Angle `2=4x°`Angle `3=3x°`Angle `4=2x°`Angle `1` `+`Angle `2` `+`Angle `3` `+`Angle `4` `=` Sum of Interior Angles `x` `+``4x` `+``3x` `+``2x` `=` `360` Substitute the values `10x` `=` `360` To solve for `x`, it needs to be alone on one side.Start by removing `10` by dividing both sides of the equation by `10`.`10``x` `=` `360` `10``x``divide10` `=` `360``divide10` `x` `=` `36` `10divide10` cancels out Check our workTo confirm our answer, substitute `x=36` to the formed equation.`x+4x+3x+2x` `=` `360` `x+4x+3x+2x` `=` `360` Substitute `x=36` `36+4(36)+3(36)+2(36)` `=` `360` `36+144+108+72` `=` `360` `360` `=` `360` Since the equation is true, the answer is correct.`x=36`Hint
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- One Step Equations – Add and Subtract
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