Question

1. (196) distribute in the expression: (3x + 2y)(4x - 5y)

a) 12x² - 10y²
b) 7x - 7xy - 3y
c) 7x - 3y
d) 12x² - 7xy - 10y²
e) 12x² + 23xy + 10y²

1. (141) solve: $\frac{5x}{4}+6=-3x$

a) $-\frac{24}{17}$
b) $-\frac{20}{19}$
c) $-\frac{17}{20}$
d) $-\frac{19}{17}$

Explanation:

Step1: Expand the first expression

Use FOIL method.
$$(3x + 2y)(4x - 5y)=3x\times4x+3x\times(- 5y)+2y\times4x+2y\times(-5y)$$
$$=12x^{2}-15xy + 8xy-10y^{2}$$
$$=12x^{2}-7xy - 10y^{2}$$

Step2: Solve the second - equation

First, get rid of the fraction. Multiply every term in the equation $\frac{5x}{4}+6=-3x$ by 4.
$$4\times\frac{5x}{4}+4\times6 = 4\times(-3x)$$
$$5x + 24=-12x$$
Then, add $12x$ to both sides.
$$5x+12x + 24=-12x+12x$$
$$17x+24 = 0$$
Subtract 24 from both sides.
$$17x+24 - 24=0 - 24$$
$$17x=-24$$
Divide both sides by 17.
$$x =-\frac{24}{17}$$

Answer:

1. None of the given options are correct for the distribution problem.
2. a. $-\frac{24}{17}$