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Math  /  Algebra

Questionx+27=4\frac{x+2}{7}=4

Studdy Solution

STEP 1

1. The equation x+27=4\frac{x+2}{7} = 4 is asking us to solve for xx.
2. This is a one-step equation involving a fraction.
3. The equation involves basic algebraic operations, specifically multiplication and subtraction.

STEP 2

1. Understand the structure of the equation.
2. Eliminate the fraction by performing algebraic operations.
3. Isolate the variable xx.
4. Check the solution by substituting it back into the original equation.

STEP 3

The equation x+27=4\frac{x+2}{7} = 4 indicates that the expression x+2x+2 divided by 7 equals 4.

STEP 4

To eliminate the fraction, multiply both sides of the equation by 7:
7×x+27=7×4 7 \times \frac{x+2}{7} = 7 \times 4
This simplifies to:
x+2=28 x + 2 = 28

STEP 5

Now, isolate xx by subtracting 2 from both sides of the equation:
x+2−2=28−2 x + 2 - 2 = 28 - 2
Simplify:
x=26 x = 26

STEP 6

Check the solution by substituting x=26x = 26 back into the original equation:
26+27=4 \frac{26+2}{7} = 4
Simplify the left-hand side:
287=4 \frac{28}{7} = 4
Since both sides are equal, the solution is verified.
The solution is:
26 \boxed{26}

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