Answer:
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
