Here are the step-by-step solutions for each problem on the worksheet.
Simplify each expression
*To simplify, use the distributive property: multiply the number outside the parentheses by each term inside.*
1. $2(-x + 4)$
* Multiply $2$ by $-x$: $2 \cdot -x = -2x$
* Multiply $2$ by $4$: $2 \cdot 4 = 8$
* Combine them:
$-2x + 8$
2. $4(3x - 4)$
* Multiply $4$ by $3x$: $4 \cdot 3x = 12x$
* Multiply $4$ by $-4$: $4 \cdot -4 = -16$
* Combine them:
$12x - 16$
3. $5(2x + 3)$
* Multiply $5$ by $2x$: $5 \cdot 2x = 10x$
* Multiply $5$ by $3$: $5 \cdot 3 = 15$
* Combine them:
$10x + 15$
4. $4(3x - 1)$
* Multiply $4$ by $3x$: $4 \cdot 3x = 12x$
* Multiply $4$ by $-1$: $4 \cdot -1 = -4$
* Combine them:
$12x - 4$
5. $3(-2x)$
* Multiply $3$ by $-2x$: $3 \cdot -2 = -6$, so keep the $x$.
* Result:
$-6x$
6. $8(-2x - 1)$
* Multiply $8$ by $-2x$: $8 \cdot -2x = -16x$
* Multiply $8$ by $-1$: $8 \cdot -1 = -8$
* Combine them:
$-16x - 8$
7. $4(6x + 9)$
* Multiply $4$ by $6x$: $4 \cdot 6x = 24x$
* Multiply $4$ by $9$: $4 \cdot 9 = 36$
* Combine them:
$24x + 36$
---
Solve each equation
*To solve, isolate $x$ on one side of the equal sign.*
8. $2 - x = 4$
* Subtract $2$ from both sides: $-x = 2$
* Divide by $-1$ (or flip the signs):
$x = -2$
9. $x + 4 = 9$
* Subtract $4$ from both sides: $x = 9 - 4$
* Result:
$x = 5$
10. $x - 10 = 12$
* Add $10$ to both sides: $x = 12 + 10$
* Result:
$x = 22$
11. $2x + 2 = 10$
* Subtract $2$ from both sides: $2x = 8$
* Divide by $2$: $x = 8 / 2$
* Result:
$x = 4$
12. $3x - 12 = 12$
* Add $12$ to both sides: $3x = 24$
* Divide by $3$: $x = 24 / 3$
* Result:
$x = 8$
13. $6x + 5 = 23$
* Subtract $5$ from both sides: $6x = 18$
* Divide by $6$: $x = 18 / 6$
* Result:
$x = 3$
14. $9x - 6 = 24$
* Add $6$ to both sides: $9x = 30$
* Divide by $9$: $x = 30 / 9$
* Simplify the fraction (divide top and bottom by 3):
$x = \frac{10}{3}$ (or $3\frac{1}{3}$)
──────────────────────────────────────
Final Answer:
1. $-2x + 8$
2. $12x - 16$
3. $10x + 15$
4. $12x - 4$
5. $-6x$
6. $-16x - 8$
7. $24x + 36$
8. $x = -2$
9. $x = 5$
10. $x = 22$
11. $x = 4$
12. $x = 8$
13. $x = 3$
14. $x = \frac{10}{3}$
Parent Tip: Review the logic above to help your child master the concept of 6th grade pre algebra worksheet.
