Question

lesson 6-2
one-step equations with rational coefficients
practice and problem solving: a/b
solve.

1. $\frac{1}{3}n = 4$

$n = \underline{\quad\quad}$

1. $y + 0.4 = 2$

$y = \underline{\quad\quad}$

1. $12 = 0.5a$

$a = \underline{\quad\quad}$

1. $-1 = \frac{1}{3}v$

$v = \underline{\quad\quad}$

1. $15.5z = -77.5$

$z = \underline{\quad\quad}$

1. $\frac{t}{-11} = 11$

$t = \underline{\quad\quad}$

1. $0.5m = 0.75$

$m = \underline{\quad\quad}$

1. $\frac{r}{4} = 250$

$r = \underline{\quad\quad}$

Explanation:

Problem 1: $\boldsymbol{\frac{1}{3}n = 4}$

Step1: Multiply both sides by 3

To isolate \( n \), multiply both sides of the equation \(\frac{1}{3}n = 4\) by 3.
\( 3\times\frac{1}{3}n = 4\times3 \)

Step2: Simplify

Simplifying both sides, we get \( n = 12 \).

Step1: Subtract 0.4 from both sides

To isolate \( y \), subtract 0.4 from both sides of the equation \( y + 0.4 = 2 \).
\( y + 0.4 - 0.4 = 2 - 0.4 \)

Step2: Simplify

Simplifying both sides, we get \( y = 1.6 \).

Step1: Divide both sides by 0.5

To isolate \( a \), divide both sides of the equation \( 12 = 0.5a \) by 0.5.
\( \frac{12}{0.5} = \frac{0.5a}{0.5} \)

Step2: Simplify

Simplifying both sides, we get \( a = 24 \).

Answer:

\( n = 12 \)

Problem 2: $\boldsymbol{y + 0.4 = 2}$