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Solve the inequality, and write the solution set in interval notation if possible. Write numbers as simplified fractions or integers.6w-71 +751The solution set is

User Rostislav Shtanko
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1 Answer

28 votes
28 votes

we have the inequality

|6W-7|+7 ≤ 1

step 1

Solve the first case (positive case)

+(6w-7)+7 ≤ 1

6w ≤ 1

w ≤ 1/6

The solution to the first inequality is (-infinite, 1/6]

step 2

Solve the second case (negative case)

-(6w-7)+7 ≤ 1

Multiply by -1 on both sides of the inequality

(6w-7)-7 ≥ -1

6w-14 ≥ -1

6w ≥ -1+14

6w ≥ 13

w ≥ 13/6

The solution to the second inequality is [13/6, infinite)

therefore

The solution toof the given inequality is

(-infinite, 1/6] ∩ [13/6, infinite)=Ф

there is no solution

User CuriousYogurt
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