Math / Algebra

QuestionSolve the inequality for $x$ . $\frac{1}{4} x+8 \leq 17$
Simplify your answer as much as possible.

Studdy Solution

STEP 1

1. The inequality $\frac{1}{4}x + 8 \leq 17$ is a linear inequality.
2. We aim to isolate the variable $x$ on one side of the inequality.
3. We will use basic algebraic operations to solve the inequality.

STEP 2

1. Isolate the term involving $x$ by removing constants from one side.
2. Solve for $x$ by performing algebraic operations.
3. Simplify the solution as much as possible.

STEP 3

Subtract 8 from both sides of the inequality to isolate the term with $x$ :
$\frac{1}{4}x + 8 - 8 \leq 17 - 8$
Simplify:
$\frac{1}{4}x \leq 9$

STEP 4

To solve for $x$ , multiply both sides of the inequality by 4 to eliminate the fraction:
$4 \times \frac{1}{4}x \leq 4 \times 9$
Simplify:
$x \leq 36$

STEP 5

The solution is already simplified. Therefore, the solution to the inequality is:
$x \leq 36$

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QuestionSolve the inequality for $x$ . $\frac{1}{4} x+8 \leq 17$
Simplify your answer as much as possible.

Studdy Solution

STEP 1

1. The inequality $\frac{1}{4}x + 8 \leq 17$ is a linear inequality.
2. We aim to isolate the variable $x$ on one side of the inequality.
3. We will use basic algebraic operations to solve the inequality.

STEP 2

1. Isolate the term involving $x$ by removing constants from one side.
2. Solve for $x$ by performing algebraic operations.
3. Simplify the solution as much as possible.

STEP 3

Subtract 8 from both sides of the inequality to isolate the term with $x$ :
$\frac{1}{4}x + 8 - 8 \leq 17 - 8$
Simplify:
$\frac{1}{4}x \leq 9$

STEP 4

To solve for $x$ , multiply both sides of the inequality by 4 to eliminate the fraction:
$4 \times \frac{1}{4}x \leq 4 \times 9$
Simplify:
$x \leq 36$

STEP 5

The solution is already simplified. Therefore, the solution to the inequality is:
$x \leq 36$

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QuestionSolve the inequality for xxx. 14x+8≤17\frac{1}{4} x+8 \leq 1741​x+8≤17Simplify your answer as much as possible.

Studdy Solution

STEP 1

1. The inequality 14x+8≤17 \frac{1}{4}x + 8 \leq 17 41​x+8≤17 is a linear inequality.2. We aim to isolate the variable x x x on one side of the inequality.3. We will use basic algebraic operations to solve the inequality.

STEP 2

1. Isolate the term involving x x x by removing constants from one side.2. Solve for x x x by performing algebraic operations.3. Simplify the solution as much as possible.

STEP 3

Subtract 8 from both sides of the inequality to isolate the term with x x x:14x+8−8≤17−8 \frac{1}{4}x + 8 - 8 \leq 17 - 8 41​x+8−8≤17−8Simplify:14x≤9 \frac{1}{4}x \leq 9 41​x≤9

STEP 4

To solve for x x x, multiply both sides of the inequality by 4 to eliminate the fraction:4×14x≤4×9 4 \times \frac{1}{4}x \leq 4 \times 9 4×41​x≤4×9Simplify:x≤36 x \leq 36 x≤36

STEP 5

The solution is already simplified. Therefore, the solution to the inequality is:x≤36 x \leq 36 x≤36

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Studdy solves anything!

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QuestionSolve the inequality for $x$ . $\frac{1}{4} x+8 \leq 17$
Simplify your answer as much as possible.

1. The inequality $\frac{1}{4}x + 8 \leq 17$ is a linear inequality.
2. We aim to isolate the variable $x$ on one side of the inequality.
3. We will use basic algebraic operations to solve the inequality.

1. Isolate the term involving $x$ by removing constants from one side.
2. Solve for $x$ by performing algebraic operations.
3. Simplify the solution as much as possible.

Subtract 8 from both sides of the inequality to isolate the term with $x$ :
$\frac{1}{4}x + 8 - 8 \leq 17 - 8$
Simplify:
$\frac{1}{4}x \leq 9$

To solve for $x$ , multiply both sides of the inequality by 4 to eliminate the fraction:
$4 \times \frac{1}{4}x \leq 4 \times 9$
Simplify:
$x \leq 36$

The solution is already simplified. Therefore, the solution to the inequality is:
$x \leq 36$