Simplify 8a − 14a − 10, Solve 3x − 7 = 11, and Factorize 2x2 + 7x + 3.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

1. Simplify the expression: $8a - 14a - 10$

Combine the like terms involving $a$ .
$8a - 14a - 10 = (8 - 14)a - 10$
Perform the subtraction.
$= -6a - 10$
The simplified expression is $\boxed{-6a - 10}$ .

2. Solve the equation: $3x - 7 = 11$
Add 7 to both sides of the equation to isolate the term with $x$ .
$3x - 7 + 7 = 11 + 7$ $3x = 18$
Divide both sides by 3 to solve for $x$ .
$\frac{3x}{3} = \frac{18}{3}$ $x = 6$
The solution to the equation is $\boxed{x = 6}$ .

3. Factorize Completely: $2x^2 + 7x + 3$
This is a quadratic expression in the form $ax^2 + bx + c$ .
Find two numbers that multiply to $ac$ and add up to $b$ .
Here, $a=2$ , $b=7$ , $c=3$ .
So, $ac = 2 \times 3 = 6$ . We need two numbers that multiply to 6 and add to 7. These numbers are 1 and 6.
Rewrite the middle term ( $7x$ ) using these two numbers ( $x$ and $6x$ ).
$2x^2 + x + 6x + 3$
Factor by grouping the first two terms and the last two terms.
$x(2x + 1) + 3(2x + 1)$
Factor out the common binomial factor $(2x + 1)$ .
$(2x + 1)(x + 3)$
The completely factorized expression is $\boxed{(2x + 1)(x + 3)}$ .

Simplify 8a - 14a - 10, Solve 3x − 7 = 11, and Factorize 2x2 + 7x + 3.