Question $0.5(2+x)=1.5$

Studdy Solution

STEP 1

1. The equation $0.5(2+x) = 1.5$ is a linear equation.
2. We are solving for the variable $x$ .
3. The equation involves basic algebraic operations, specifically distribution and solving a simple linear equation.

STEP 2

1. Distribute the constant $0.5$ across the terms inside the parentheses.
2. Simplify the equation to isolate the variable $x$ .
3. Solve for $x$ .
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute $0.5$ to both terms inside the parentheses:
$0.5 \times 2 + 0.5 \times x = 1.5$
This simplifies to:
$1 + 0.5x = 1.5$

STEP 4

Subtract 1 from both sides of the equation to isolate the term with $x$ :
$0.5x = 1.5 - 1$
Simplify the right-hand side:
$0.5x = 0.5$

STEP 5

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

STEP 6

Check the solution by substituting $x = 1$ back into the original equation:
Substitute $x = 1$ :
$0.5(2 + 1) = 1.5$
Simplify inside the parentheses:
$0.5 \times 3 = 1.5$
Simplify the multiplication:
$1.5 = 1.5$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{1}$

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