QuestionDecember 12, 2025

13. Which equation has infinitely many solutions? a) 17+4x=8x+11-4x b) 15x+12-4x=19+9x-7x C) 9-0.7x=5.1x+17-8 d) 13x-2x=22

13. Which equation has infinitely many solutions? a) 17+4x=8x+11-4x b) 15x+12-4x=19+9x-7x C) 9-0.7x=5.1x+17-8 d) 13x-2x=22
13. Which equation has infinitely many solutions?
a) 17+4x=8x+11-4x
b) 15x+12-4x=19+9x-7x
C) 9-0.7x=5.1x+17-8
d) 13x-2x=22

Solution
4.0(204 votes)

Answer

None of the given equations has infinitely many solutions. Explanation 1. Simplify each equation a) 17 + 4x = 8x + 11 - 4x \implies 17 + 4x = 4x + 11 b) 15x + 12 - 4x = 19 + 9x - 7x \implies 11x + 12 = 2x + 19 c) 9 - 0.7x = 5.1x + 17 - 8 \implies 9 - 0.7x = 5.1x + 9 d) 13x - 2x = 22 \implies 11x = 22 2. Check for infinitely many solutions (identical sides) Only option a) can be simplified to 17 = 11, which is false, so not infinite. Option b): 11x + 12 = 2x + 19 \implies 9x = 7 \implies x = \frac{7}{9}, one solution. Option c): 9 - 0.7x = 5.1x + 9 \implies -0.7x = 5.1x \implies -0.7x - 5.1x = 0 \implies -5.8x = 0 \implies x = 0, one solution. Option d): 11x = 22 \implies x = 2, one solution. 3. Re-examine for identical equations None of the equations simplify to an identity like a = a for all x.

Explanation

1. Simplify each equation<br /> a) $17 + 4x = 8x + 11 - 4x \implies 17 + 4x = 4x + 11$<br /> b) $15x + 12 - 4x = 19 + 9x - 7x \implies 11x + 12 = 2x + 19$<br /> c) $9 - 0.7x = 5.1x + 17 - 8 \implies 9 - 0.7x = 5.1x + 9$<br /> d) $13x - 2x = 22 \implies 11x = 22$<br /><br />2. Check for infinitely many solutions (identical sides)<br /> Only option a) can be simplified to $17 = 11$, which is false, so not infinite.<br /> Option b): $11x + 12 = 2x + 19 \implies 9x = 7 \implies x = \frac{7}{9}$, one solution.<br /> Option c): $9 - 0.7x = 5.1x + 9 \implies -0.7x = 5.1x \implies -0.7x - 5.1x = 0 \implies -5.8x = 0 \implies x = 0$, one solution.<br /> Option d): $11x = 22 \implies x = 2$, one solution.<br /><br />3. Re-examine for identical equations<br /> None of the equations simplify to an identity like $a = a$ for all $x$.
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