Question

Which statement about the equation 5q+4−11/2=2q+3/2(2q−1) is true?
A. Since 5q+4−11/2 simplifies to 5q, and 2q+3/2(2q−1) simplifies to 5q, the equation has no solution.
B. Since 5q+4−11/2 simplifies to 5q - 3/2, and 2q + 3/2(2q-1) simplifies to 5q-3/2, the equation has infinitely many solutions.
C. Since 5q+4-11/2 simplifies to 5q-19/2, and 2q+3/2(2q-1)simplifies to 5q-3/2, the equation has one solution.
D. The equation cannot be simplified since a variable is on both sides of the equal sign.

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which statement about the equation

5q+4−11/2=2q+3/2(2q−1) is true

A. Since 5q+4−11/2 simplifies to 5q, and 2q+3/2(2q−1) simplifies to 5q, the equation has no solution.

B. Since 5q+4−11/2 simplifies to 5q - 3/2, and 2q + 3/2(2q-1) simplifies to 5q-3/2, the equation has infinitely many solutions.

C. Since 5q+4-11/2 simplifies to 5q-19/2, and 2q+3/2(2q-1)simplifies to 5q-3/2, the equation has one solution.

D. The equation cannot be simplified since a variable is on both sides of the equal sign.

EVALUATION

Here the given equation is

$\displaystyle \sf{5q + 4 - \frac{11}{2} = 2q + \frac{3}{2} \bigg(2q - 1 \bigg) }$

We now simplify it as below :

LHS of the equation

$\displaystyle \sf{5q + 4 - \frac{11}{2} }$

$\displaystyle \sf{ = 5q + \frac{8 - 11}{2} }$

$\displaystyle \sf{ = 5q - \frac{3}{2} }$

RHS of the equation

$\displaystyle \sf{ = 2q + \frac{3}{2} \bigg(2q - 1 \bigg) }$

$\displaystyle \sf{ = 2q + 3q - \frac{3}{2} }$

$\displaystyle \sf{ = 5q - \frac{3}{2} }$

So both sides are equal

Hence the equation is satisfied for all real values of q

FINAL ANSWER

Hence the correct option is

B. Since 5q+4−11/2 simplifies to 5q - 3/2, and 2q + 3/2(2q-1) simplifies to 5q-3/2, the equation has infinitely many solutions.

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