Answer:
q = infinite amount of solutions
Step-by-step explanation:
Step 1: Write equation
8q + 12 = 4(3 + 2q)
Step 2: Solve for q
- Distribute 4: 8q + 12 = 12 + 8q
- Subtract 8q on both sides: 12 = 12
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- Distribute 4: 8q + 12 = 12 + 8q
- Subtract 12 on both sides 8q = 8q
- Divide both sides by 8: q = q
We see here that you can plug in any number q and it would render the equation true. You can also look at it as 2 linear lines that are same, and the same line has infinite amount of solutions.
Step 3: Check
Plug in q to verify it's a solution.
8(0) + 12 = 4(3 + 2(0))
0 + 12 = 4(3 + 0)
12 = 4(3)
12 = 12
8(1) + 12 = 4(3 + 2(1))
8 + 12 = 4(3 + 2)
20 = 4(5)
20 = 20
We also see in the check step that any value q works.
