Here are the step-by-step solutions for simplifying each algebraic expression.
1) $-3(9 + 6w) + 8$
* Distribute the $-3$: $-3 \times 9 = -27$ and $-3 \times 6w = -18w$.
* Expression becomes: $-27 - 18w + 8$.
* Combine constants: $-27 + 8 = -19$.
* Result:
$-18w - 19$
2) $4(-5y - 9)$
* Distribute the $4$: $4 \times -5y = -20y$ and $4 \times -9 = -36$.
* Result:
$-20y - 36$
3) $9(-5 + 3c)$
* Distribute the $9$: $9 \times -5 = -45$ and $9 \times 3c = 27c$.
* Result:
$27c - 45$
4) $-3(6 - 5r)$
* Distribute the $-3$: $-3 \times 6 = -18$ and $-3 \times -5r = +15r$.
* Result:
$15r - 18$
5) $8(-9p - 2) + 7$
* Distribute the $8$: $8 \times -9p = -72p$ and $8 \times -2 = -16$.
* Expression becomes: $-72p - 16 + 7$.
* Combine constants: $-16 + 7 = -9$.
* Result:
$-72p - 9$
6) $2(-4 + 8h)$
* Distribute the $2$: $2 \times -4 = -8$ and $2 \times 8h = 16h$.
* Result:
$16h - 8$
7) $-8(-3 + 6w) - 7w$
* Distribute the $-8$: $-8 \times -3 = +24$ and $-8 \times 6w = -48w$.
* Expression becomes: $24 - 48w - 7w$.
* Combine $w$ terms: $-48w - 7w = -55w$.
* Result:
$-55w + 24$
8) $7(-9r - 5)$
* Distribute the $7$: $7 \times -9r = -63r$ and $7 \times -5 = -35$.
* Result:
$-63r - 35$
9) $-6s - 7(2 + 9s)$
* Distribute the $-7$: $-7 \times 2 = -14$ and $-7 \times 9s = -63s$.
* Expression becomes: $-6s - 14 - 63s$.
* Combine $s$ terms: $-6s - 63s = -69s$.
* Result:
$-69s - 14$
10) $-6 + 4(-9y + 8)$
* Distribute the $4$: $4 \times -9y = -36y$ and $4 \times 8 = 32$.
* Expression becomes: $-6 - 36y + 32$.
* Combine constants: $-6 + 32 = 26$.
* Result:
$-36y + 26$
Final Answer:
1) $-18w - 19$
2) $-20y - 36$
3) $27c - 45$
4) $15r - 18$
5) $-72p - 9$
6) $16h - 8$
7) $-55w + 24$
8) $-63r - 35$
9) $-69s - 14$
10) $-36y + 26$
Parent Tip: Review the logic above to help your child master the concept of sixth grade algebra worksheet.
