directions: solve each equation. show all steps! 1. -4x - 7 - 3x + 4 = 25 2. -4(7a + 5) = -160 3. 3k + 2(5k…

Explanation:

Step1: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side of the equation $-4x - 7-3x + 4 = 25$. $(-4x-3x)+(-7 + 4)=25$, which simplifies to $-7x-3 = 25$.

Step2: Isolate the variable term

Add 3 to both sides of the equation: $-7x-3 + 3=25 + 3$, resulting in $-7x=28$.

Step3: Solve for $x$

Divide both sides of the equation by - 7: $\frac{-7x}{-7}=\frac{28}{-7}$, so $x=-4$.

Answer:

$x = - 4$

Explanation:

Step1: Distribute the - 4

For the equation $-4(7a + 5)=-160$, use the distributive property $a(b + c)=ab+ac$. $-4\times7a-4\times5=-160$, which gives $-28a-20=-160$.

Step2: Isolate the variable term

Add 20 to both sides of the equation: $-28a-20 + 20=-160 + 20$, resulting in $-28a=-140$.

Step3: Solve for $a$

Divide both sides of the equation by - 28: $\frac{-28a}{-28}=\frac{-140}{-28}$, so $a = 5$.

Answer:

$a = 5$

Explanation:

Step1: Distribute the 2

For the equation $3k+2(5k - 3)=7$, use the distributive property: $3k+2\times5k-2\times3 = 7$, which simplifies to $3k + 10k-6 = 7$.

Step2: Combine like - terms

Combine the $k$ terms on the left - hand side: $(3k + 10k)-6 = 7$, or $13k-6 = 7$.

Step3: Isolate the variable term

Add 6 to both sides of the equation: $13k-6 + 6=7 + 6$, resulting in $13k=13$.

Step4: Solve for $k$

Divide both sides of the equation by 13: $\frac{13k}{13}=\frac{13}{13}$, so $k = 1$.

Answer:

$k = 1$

Explanation:

Step1: Distribute the 3

For the equation $-79=7w + 3(4w-1)$, use the distributive property: $-79=7w+3\times4w-3\times1$, which simplifies to $-79=7w + 12w-3$.

Step2: Combine like - terms

Combine the $w$ terms on the right - hand side: $-79=(7w + 12w)-3$, or $-79=19w-3$.

Step3: Isolate the variable term

Add 3 to both sides of the equation: $-79 + 3=19w-3 + 3$, resulting in $-76=19w$.

Step4: Solve for $w$

Divide both sides of the equation by 19: $\frac{-76}{19}=\frac{19w}{19}$, so $w=-4$.

Answer:

$w=-4$

Explanation:

Step1: Distribute the - 4

For the equation $9-4(2p - 1)=41$, use the distributive property: $9-4\times2p+4\times1 = 41$, which simplifies to $9-8p + 4=41$.

Step2: Combine like - terms

Combine the constant terms on the left - hand side: $(9 + 4)-8p=41$, or $13-8p=41$.

Step3: Isolate the variable term

Subtract 13 from both sides of the equation: $13-8p-13=41-13$, resulting in $-8p=28$.

Step4: Solve for $p$

Divide both sides of the equation by - 8: $\frac{-8p}{-8}=\frac{28}{-8}$, so $p=-\frac{7}{2}$.

Answer:

$p=-\frac{7}{2}$

Explanation:

Step1: Distribute the - 3

For the equation $y-3(2y - 7)=76$, use the distributive property: $y-3\times2y+3\times7 = 76$, which simplifies to $y-6y + 21=76$.

Step2: Combine like - terms

Combine the $y$ terms on the left - hand side: $(y-6y)+21=76$, or $-5y+21=76$.

Step3: Isolate the variable term

Subtract 21 from both sides of the equation: $-5y+21-21=76-21$, resulting in $-5y=55$.

Step4: Solve for $y$

Divide both sides of the equation by - 5: $\frac{-5y}{-5}=\frac{55}{-5}$, so $y=-11$.

Answer:

$y=-11$