Question $0.5(2+x)=1.5$

Studdy Solution

STEP 1

1. The equation $0.5(2+x) = 1.5$ is asking us to solve for $x$ .
2. This is a linear equation involving basic algebraic operations.
3. We will use the distributive property and inverse operations to solve for $x$ .

STEP 2

1. Apply the distributive property to remove parentheses.
2. Isolate the variable $x$ by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

Apply the distributive property to the left side of the equation:
$0.5 \times 2 + 0.5 \times x = 1.5$
Simplify:
$1 + 0.5x = 1.5$

STEP 4

Subtract 1 from both sides to isolate the term with $x$ :
$1 + 0.5x - 1 = 1.5 - 1$
Simplify:
$0.5x = 0.5$

STEP 5

Divide both sides by 0.5 to solve for $x$ :
$\frac{0.5x}{0.5} = \frac{0.5}{0.5}$
Simplify:
$x = 1$

STEP 6

Check the solution by substituting $x = 1$ back into the original equation:
$0.5(2 + 1) = 1.5$
Simplify the left side:
$0.5 \times 3 = 1.5$
Check if both sides are equal:
$1.5 = 1.5$
Yes, both sides are equal.
The solution is:
$\boxed{1}$

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