Solve 2a-3+8+4aleq4a+11/2

$$2 a - 3 + 8 + 4 a \leq 4 a + \frac { 11 } { 2 }$$

Solve for a

$$a\leq \frac{1}{4}$$

Solution Steps

Add -3 and 8 to get 5.

$$2a+5+4a\leq 4a+\frac{11}{2}$$

Combine 2a and 4a to get 6a.

$$6a+5\leq 4a+\frac{11}{2}$$

Subtract 4a from both sides.

$$6a+5-4a\leq \frac{11}{2}$$

Combine 6a and -4a to get 2a.

$$2a+5\leq \frac{11}{2}$$

Subtract 5 from both sides.

$$2a\leq \frac{11}{2}-5$$

Convert 5 to fraction \frac{10}{2}.

$$2a\leq \frac{11}{2}-\frac{10}{2}$$

Since \frac{11}{2} and \frac{10}{2} have the same denominator, subtract them by subtracting their numerators.

$$2a\leq \frac{11-10}{2}$$

Subtract 10 from 11 to get 1.

$$2a\leq \frac{1}{2}$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$a\leq \frac{\frac{1}{2}}{2}$$

Express \frac{\frac{1}{2}}{2} as a single fraction.

$$a\leq \frac{1}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$a\leq \frac{1}{4}$$