Question

unit 1c study guide
question 4
which inequalities have no solution? select all that apply.
a) $3x + 11 < 3x + 5$
b) $2(m - 3) - 5 > 2(m + 3) - 5$
c) $4(t + 4) > 4(t - 4)$
d) $3x - 11 < 3x - 5$
e) $9(n - 4) + 5 > 7(n + 1) + 2n$

Explanation:

Step1: Analyze Option A

Start with inequality \(3x + 11<3x + 5\). Subtract \(3x\) from both sides: \(3x - 3x+ 11<3x - 3x + 5\), which simplifies to \(11 < 5\). This is false, so no solution.

Step2: Analyze Option B

Expand \(2(m - 3)-5>2(m + 3)-5\): \(2m-6 - 5>2m + 6 - 5\), so \(2m-11>2m + 1\). Subtract \(2m\): \(2m - 2m-11>2m - 2m + 1\), giving \(-11>1\), false, no solution.

Step3: Analyze Option C

Expand \(4(t + 4)>4(t - 4)\): \(4t+16>4t - 16\). Subtract \(4t\): \(4t - 4t+16>4t - 4t - 16\), so \(16>-16\), true, has solutions.

Step4: Analyze Option D

Inequality \(3x - 11<3x - 5\). Subtract \(3x\): \(3x - 3x-11<3x - 3x - 5\), giving \(-11 < -5\), true, has solutions.

Step5: Analyze Option E

Expand \(9(n - 4)+5>7(n + 1)+2n\): \(9n-36 + 5>7n + 7+2n\), so \(9n-31>9n + 7\). Subtract \(9n\): \(9n - 9n-31>9n - 9n + 7\), giving \(-31>7\), false, no solution.

Answer:

A. \(3x + 11 < 3x + 5\), B. \(2(m - 3) - 5 > 2(m + 3) - 5\), E. \(9(n - 4) + 5 > 7(n + 1) + 2n\)