Question

1. solve each equation. check your solutions

a. $2.5 = 0.5y$

Explanation:

Step1: Divide both sides by 0.5

To solve for \( y \) in the equation \( 2.5 = 0.5y \), we divide both sides of the equation by \( 0.5 \). This is based on the division property of equality, which states that if we divide both sides of an equation by the same non - zero number, the equation remains true.

So we have \( \frac{2.5}{0.5}=\frac{0.5y}{0.5} \)

Step2: Simplify both sides

Simplifying the left - hand side: \( \frac{2.5}{0.5}=5 \)

Simplifying the right - hand side: \( \frac{0.5y}{0.5}=y \) (because any non - zero number divided by itself is 1, so \( 0.5\div0.5 = 1\), and \( 1\times y=y \))

So we get \( y = 5 \)

Step3: Check the solution

Substitute \( y = 5 \) back into the original equation \( 2.5=0.5y \)

The right - hand side becomes \( 0.5\times5 = 2.5 \), which is equal to the left - hand side of the original equation.

Answer:

\( y = 5 \)