Question

c. $21.8 = 6.4x - 3$ d. $4\frac{1}{2} = -\frac{1}{3}t + 6\frac{1}{2}$ e. $-6.4 = 1.6(b - 2.8)$ f. $-1\frac{1}{2} = \frac{r - 0.5}{4}$

Explanation:

Part c: Solve \( 21.8 = 6.4x - 3 \)

Step 1: Add 3 to both sides

To isolate the term with \( x \), we add 3 to both sides of the equation.
\( 21.8 + 3 = 6.4x - 3 + 3 \)
\( 24.8 = 6.4x \)

Step 2: Divide by 6.4

Divide both sides by 6.4 to solve for \( x \).
\( x = \frac{24.8}{6.4} \)
\( x = 3.875 \)

Step 1: Subtract \( 6\frac{1}{2} \) from both sides

First, convert mixed numbers to decimals (or keep as fractions). \( 4\frac{1}{2} = 4.5 \), \( 6\frac{1}{2} = 6.5 \).
\( 4.5 - 6.5 = -\frac{1}{3}t + 6.5 - 6.5 \)
\( -2 = -\frac{1}{3}t \)

Step 2: Multiply by -3

Multiply both sides by -3 to solve for \( t \).
\( t = (-2) \times (-3) \)
\( t = 6 \)

Step 1: Divide by 1.6

Divide both sides by 1.6 to isolate the parentheses.
\( \frac{-6.4}{1.6} = \frac{1.6(b - 2.8)}{1.6} \)
\( -4 = b - 2.8 \)

Step 2: Add 2.8 to both sides

Add 2.8 to both sides to solve for \( b \).
\( -4 + 2.8 = b - 2.8 + 2.8 \)
\( b = -1.2 \)

Answer:

\( x = 3.875 \)

Part d: Solve \( 4\frac{1}{2}=-\frac{1}{3}t + 6\frac{1}{2} \)