Question

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7.2k = -57.6
\\(\frac{5}{6}n - 4 = 8\\)
4x - 7 = 29
4z + 15 = 1
\\(\frac{k}{-8} + 6 = 1\\)
\\(\frac{k + 3}{-9} = 6\\)
combine like terms or apply distributive property before solving
1.6p - 4 = -9
3(x + 2) = 12
5(7 - 5t) = -40

Explanation:

Let's solve each equation one by one:

1. Solve \( 7.2k = -57.6 \)

Step 1: Isolate \( k \) by dividing both sides by 7.2

To solve for \( k \), we divide both sides of the equation \( 7.2k = -57.6 \) by \( 7.2 \).

$$ k=\frac{-57.6}{7.2} $$

Step 2: Calculate the value of \( k \)

$$ k = - 8 $$

Step 1: Add 4 to both sides

First, we add 4 to both sides of the equation \( \frac{5}{6}n - 4 = 8 \) to isolate the term with \( n \).

$$ \frac{5}{6}n-4 + 4=8 + 4 $$

$$ \frac{5}{6}n=12 $$

Step 2: Multiply both sides by \( \frac{6}{5} \)

To solve for \( n \), we multiply both sides by the reciprocal of \( \frac{5}{6} \), which is \( \frac{6}{5} \).

$$ n = 12\times\frac{6}{5} $$

$$ n=\frac{72}{5}=14.4 $$

Step 1: Add 7 to both sides

Add 7 to both sides of the equation \( 4x - 7 = 29 \) to isolate the term with \( x \).

$$ 4x-7 + 7=29 + 7 $$

$$ 4x=36 $$

Step 2: Divide both sides by 4

Divide both sides by 4 to solve for \( x \).

$$ x=\frac{36}{4} $$

$$ x = 9 $$

Answer:

\( k=-8 \)

2. Solve \( \frac{5}{6}n - 4 = 8 \)