If 11c – 7 = 8, what is the value of 33c – 21?
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Solution
Although you could solve the first equation for c and substitute that value into the given expression, look at the relationship between the equation and the expression. 33c – 21 is exactly three times 11c – 7. Therefore, the value of 33c – 21 will be three times the value of 11c – 7; 3(8) = 24; 33c – 21 = 24
If 8x + 4 = 14, what is the value of 4x + 2?
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Solution
Although you could solve the first equation for x and substitute that value into the given expression, look at the relationship between the equation and the expression; 4x + 2 is exactly half of 8x + 4. Therefore, the value of 4x + 2 will be half the value of 8x + 4; \(\frac{14}{2}\) = 7; 4x + 2 = 7.
If 9x + 8⁄3 = (8⁄3)x + 9, what is the value of (3⁄8)x?
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Solution
Subtract (8⁄3)x and 8⁄3 from both sides of the equation: 9x + 8⁄3 = (8⁄3)x + 9,\(\frac{19}{3}\)x =\(\frac{19}{3}\). Multiply both sides of the equation by \(\frac{3}{19}\) : (\(\frac{3}{19}\))(\(\frac{3}{19}\)x) = (\(\frac{19}{3}\))(\(\frac{19}{3}\)),x = 1. Since x = 1,(3⁄8)x =3⁄8(1) =3⁄8.
If 3x – 8 =\(\frac{9x+5}{2}\), what is the value of x + 7?
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Solution
First, cross multiply: (2)(3x – 8) = 9x + 5, 6x – 16 = 9x + 5. Subtract 6x from both sides of the equation and subtract 5 from both sides of the equation, 6x – 16 = 9x + 5, 3x = –21. Divide by 3 to solve for x:\(\frac{3x}{3}=\frac{-21}{3}\), x = –7. Since x = –7, x + 7 = –7 + 7 = 0.
If (1⁄2)x + 6 = –x – 3, what is the value of –2x?
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Solution
Add x to both sides of the equation and subtract 6 from both sides of the equation; (1⁄2)x + 6 = –x – 3,(3⁄2)x = –9. Multiply both sides of the equation by 2⁄3 to isolate x: (2⁄3)(3⁄2x) = –9(2⁄3), x = –6.Since x = –6, –2x = –2(–6) = 12.
If \(\frac{5g}{g}=\frac{g+7}{g-1}\), what is the value of g?
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Solution
First, reduce \(\frac{5g}{g}\) by canceling g from the numerator and denominator: \(\frac{5g}{g}\) = 5⁄1. Now, cross multiply and solve for g: (5)(g – 1) = (1)(g + 7), 5g – 5 = g + 7, 4g – 5 = 7, 4g = 12, g = 3.
If \(\frac{6}{-y-1}=\frac{10}{-2y-3}\), what is the value of y?
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Solution
Cross multiply and solve for y: (6)(–2y – 3) = (10)(–y – 1), –12y – 18 = –10y – 10, –2y – 18 = –10, –2y = 8, y = –4.
If \(\frac{4a+4}{7}=\frac{2-3a}{4}\) , what is the value of a?
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Solution
Cross multiply and solve for a: (4a + 4)(4) = (7)(–2 + 3a), 16a + 16 = –14 + 21a, 16a + 30 = 21a, 5a = 30, a = 6.
If \(\frac{10x}{7}=\frac{5x-10}{3}\), what is the value of x?
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Solution
Cross multiply and solve for x: (10x)(3) = (7)(5x – 10), 30x = 35x – 70, –5x = –70, x = 14.
If \(\frac{w}{w+8}=-\frac{6}{18}\), what is the value of w?
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Solution
Cross multiply and solve for w: (w)(18) = (–6)(w + 8), 18w = –6w – 48, 24w = –48,w = –2.