Math  /  Algebra

Question5. Solve the inequality. Use a calculator as needed. 12m+6>4+912-\frac{1}{2} m+6>-4+9 \frac{1}{2} m<1m<1 m>92m>\frac{9}{2} m>1.1m>1.1 m<0.2m<0.2

Studdy Solution

STEP 1

1. The inequality given is 12m+6>4+912-\frac{1}{2} m + 6 > -4 + 9 \frac{1}{2}.
2. We need to isolate mm to solve the inequality.
3. We will use basic algebraic operations to simplify and solve the inequality.
4. A calculator may be used for arithmetic calculations if needed.
5. We will verify which of the provided options satisfies the inequality.

STEP 2

1. Simplify the right-hand side of the inequality.
2. Isolate the variable mm on one side of the inequality.
3. Solve for mm.
4. Compare the solution with the given options to determine the correct inequality.

STEP 3

Simplify the constant terms on the right-hand side of the inequality. 4+912=4+9.5=5.5 -4 + 9 \frac{1}{2} = -4 + 9.5 = 5.5

STEP 4

Rewrite the inequality with the simplified right-hand side. 12m+6>5.5 -\frac{1}{2} m + 6 > 5.5

STEP 5

Subtract 6 from both sides to isolate the term involving mm. 12m+66>5.56 -\frac{1}{2} m + 6 - 6 > 5.5 - 6 12m>0.5 -\frac{1}{2} m > -0.5

STEP 6

Multiply both sides by 2-2 to solve for mm, remembering to reverse the inequality sign when multiplying by a negative number. m<0.5×2 m < -0.5 \times -2 m<1 m < 1

STEP 7

Compare the solution m<1m < 1 with the provided options: - m<1m < 1: This is correct. - m>92m > \frac{9}{2}: This is incorrect. - m>1.1m > 1.1: This is incorrect. - m<0.2m < 0.2: This is incorrect.
Therefore, the correct answer is m<1m < 1.
Solution: m<1m < 1

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