Math  /  Algebra

QuestionSolve the inequality. 27y4-\frac{2}{7} y \leq 4
The solution set is {y\{y \mid \square

Studdy Solution

STEP 1

1. The inequality 27y4 -\frac{2}{7} y \leq 4 involves solving for the variable y y .
2. This is a linear inequality.
3. Solving the inequality will involve basic algebraic operations, specifically multiplication and division.
4. The inequality sign may change direction if we multiply or divide by a negative number.

STEP 2

1. Isolate the variable y y on one side of the inequality.
2. Solve the inequality by performing algebraic operations.
3. Write the solution set in set-builder notation.

STEP 3

To isolate y y , we need to eliminate the fraction. We will multiply both sides of the inequality by the reciprocal of 27 -\frac{2}{7} , which is 72 -\frac{7}{2} .

STEP 4

Multiply both sides by 72 -\frac{7}{2} . Remember, multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign:
y4×72 y \geq 4 \times -\frac{7}{2}

STEP 5

Calculate the right side:
y282 y \geq -\frac{28}{2}
Simplify:
y14 y \geq -14

STEP 6

Write the solution set in set-builder notation:
The solution set is {yy14}\{ y \mid y \geq -14 \}.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord