1a. write an inequality with the solution x < 12. the inequality should have the variable on both sides, a decimal coefficient of the variable on the left side, and a decimal anywhere on the right side. one of the decimals should be written in tenths, the other in hundredths.

1b. write an inequality with the solution x ≥ 4. the inequality should have the variable on both sides, a fractional coefficient of the variable on the left side, and a fraction anywhere on the right side.

1a. 1.08x + 0.1 < 1.1 + x is equivalent to x < 12

1b. x/4 + ¼ ≥ 5/4 + x is equivalent to x ≥ 4

Step-by-step explanation:

1a.

Required:

Write an inequality with the solution x < 12

Note that the inequality should have the variable on both sides

Follow the highlighted steps;

Step 1: Write out the inequality

x < 12

Step 2: Divide both sides by 12

x/12 < 12/12

x/12 < 1

(To make a decimal coefficient of the variable on the left side)

Step 3: Convert fraction to decimal

0.08x < 1

To have one of the decimals should be written in tenths and the other in hundredths, perform step 4 and 5

Step 4: Add x to both sides

x + 0.08x < 1 + x

1.08x < 1 + x

Step 5: Add 0.1 to both sides

1.08x + 0.1 < 1 + x + 0.1

1.08x + 0.1 < 1.1 + x

Hence, equivalence of x < 12 is 1.08x + 0.1 < 1.1 + x

1b. Required:

Write an inequality with the solution x ≥ 4

Note that the inequality should have the variable on both sides

Follow the highlighted steps;

Step 1: Divide both side by 4

x/4 ≥ 4/4

x/4 ≥ 1 -- now, we have a fraction coefficient on the left hand side

To get a variable on the right side, do step 2

Step 2: add x to both sides

x/4 + x ≥ 1 + x

To get a fraction anywhere on the right side, do step 3

Step 3: Add ¼ to both sides

¼x + x + ¼ ≥ ¼ + 1 + x

¼x + x + ¼ ≥ 5/4 + x

5x/4 + ¼ ≥ 5/4 + x

Hence, equivalence of x ≥ 4 is 5x/4 + ¼ ≥ 5/4 + x