Math  /  Algebra

Question6(x+2)7x86(x+2)-7 x \geq 8

Studdy Solution

STEP 1

1. The inequality 6(x+2)7x86(x+2)-7 x \geq 8 involves a linear expression in xx.
2. Solving the inequality requires isolating the variable xx on one side.
3. The solution to the inequality will be a range of values for xx.

STEP 2

1. Expand and simplify the left-hand side of the inequality.
2. Collect like terms involving xx.
3. Isolate xx and solve the inequality.
4. Express the solution in interval notation.

STEP 3

Expand the left-hand side of the inequality 6(x+2)7x6(x+2)-7x.
6(x+2)7x8 6(x+2) - 7x \geq 8 6x+127x8 6x + 12 - 7x \geq 8

STEP 4

Combine like terms involving xx.
6x+127x8 6x + 12 - 7x \geq 8 x+128 -x + 12 \geq 8

STEP 5

Isolate the variable xx by moving the constant term to the right-hand side.
x+128 -x + 12 \geq 8 x812 -x \geq 8 - 12 x4 -x \geq -4

STEP 6

Solve for xx by dividing both sides by 1-1, remembering to reverse the inequality sign.
x4 -x \geq -4 x4 x \leq 4

STEP 7

Express the solution in interval notation.
x4    x(,4] x \leq 4 \implies x \in (-\infty, 4]
Solution: The solution to the inequality 6(x+2)7x86(x+2)-7x \geq 8 is x(,4]x \in (-\infty, 4].

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