Here are the step-by-step solutions for each linear equation.
1) $5x + 2(2x - 4) = 55$
* Distribute the 2 into the parentheses: $5x + 4x - 8 = 55$
* Combine like terms ($5x$ and $4x$): $9x - 8 = 55$
* Add 8 to both sides: $9x = 63$
* Divide by 9:
$x = 7$
2) $7x + 4(x - 9) = 41$
* Distribute the 4: $7x + 4x - 36 = 41$
* Combine like terms: $11x - 36 = 41$
* Add 36 to both sides: $11x = 77$
* Divide by 11:
$x = 7$
3) $3x + 2(x - 6) = 33$
* Distribute the 2: $3x + 2x - 12 = 33$
* Combine like terms: $5x - 12 = 33$
* Add 12 to both sides: $5x = 45$
* Divide by 5:
$x = 9$
4) $4x + 3(3x + 7) = 86$
* Distribute the 3: $4x + 9x + 21 = 86$
* Combine like terms: $13x + 21 = 86$
* Subtract 21 from both sides: $13x = 65$
* Divide by 13:
$x = 5$
5) $2x + 5(4x - 7) = 75$
* Distribute the 5: $2x + 20x - 35 = 75$
* Combine like terms: $22x - 35 = 75$
* Add 35 to both sides: $22x = 110$
* Divide by 22:
$x = 5$
6) $97 = 7x + 2(x + 8)$
* Distribute the 2: $97 = 7x + 2x + 16$
* Combine like terms: $97 = 9x + 16$
* Subtract 16 from both sides: $81 = 9x$
* Divide by 9:
$x = 9$
7) $6x + 5(2x - 7) = 45$
* Distribute the 5: $6x + 10x - 35 = 45$
* Combine like terms: $16x - 35 = 45$
* Add 35 to both sides: $16x = 80$
* Divide by 16:
$x = 5$
8) $63 = 6x + 3(3x - 4)$
* Distribute the 3: $63 = 6x + 9x - 12$
* Combine like terms: $63 = 15x - 12$
* Add 12 to both sides: $75 = 15x$
* Divide by 15:
$x = 5$
9) $3x + 4(x + 6) = 59$
* Distribute the 4: $3x + 4x + 24 = 59$
* Combine like terms: $7x + 24 = 59$
* Subtract 24 from both sides: $7x = 35$
* Divide by 7:
$x = 5$
10) $82 = 2x + 2(3x + 5)$
* Distribute the 2: $82 = 2x + 6x + 10$
* Combine like terms: $82 = 8x + 10$
* Subtract 10 from both sides: $72 = 8x$
* Divide by 8:
$x = 9$
Final Answer:
1) x = 7
2) x = 7
3) x = 9
4) x = 5
5) x = 5
6) x = 9
7) x = 5
8) x = 5
9) x = 5
10) x = 9
Parent Tip: Review the logic above to help your child master the concept of expressions and equations worksheet 8th grade.
