Math

QuestionSolve the inequality: 21x185x+1421 x - 18 \leq 5 x + 14. Subtract 5x5 x and simplify.

Studdy Solution

STEP 1

Assumptions1. The given inequality is 21x185x+1421x -18 \leq5x +14 . We are allowed to perform the same operation on both sides of the inequality to maintain the equality

STEP 2

First, we need to isolate the variable xx on one side of the inequality. We can do this by subtracting 5x5x from both sides of the inequality.
21x5x185x+145x21x -5x -18 \leq5x +14 -5x

STEP 3

Now, simplify the inequality by combining like terms.
16x181416x -18 \leq14

STEP 4

Next, we need to isolate xx by adding 1818 to both sides of the inequality.
16x18+1814+1816x -18 +18 \leq14 +18

STEP 5

implify the inequality by combining like terms.
16x3216x \leq32

STEP 6

Finally, to solve for xx, we divide both sides of the inequality by 1616.
16x163216\frac{16x}{16} \leq \frac{32}{16}

STEP 7

implify to find the solution for xx.
x2x \leq2So, the solution to the inequality is x2x \leq2.

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