Solve the following equations for x: 1) 6(3x−4) = −4(x+6) 2) 4 − 7x = 3x + 4 3) 6x − 2 = 4x − 1 4) 3(2x+5)…

Question

Solve the following equations for x: 1) 6(3x−4) = −4(x+6) 2) 4 − 7x = 3x + 4 3) 6x − 2 = 4x − 1 4) 3(2x+5) = 2(x−5) + 13

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the given equations:

$6(3x-4) = -4(x+6)$

Distribute the numbers on both sides of the equation.
$18x - 24 = -4x - 24$
Add $4x$ to both sides to collect $x$ terms.
$18x + 4x - 24 = -24$ $22x - 24 = -24$
Add 24 to both sides to isolate the $x$ term.
$22x = -24 + 24$ $22x = 0$
Divide by 22 to solve for $x$ .
$x = \frac{0}{22}$ $x = 0$
The truth set is $\boxed{\{0\}}$ .
1. $4 - 7x = 3x + 4$
Add $7x$ to both sides to collect $x$ terms.
$4 = 3x + 7x + 4$ $4 = 10x + 4$
Subtract 4 from both sides to isolate the $x$ term.
$4 - 4 = 10x$ $0 = 10x$
Divide by 10 to solve for $x$ .
$x = \frac{0}{10}$ $x = 0$
The truth set is $\boxed{\{0\}}$ .
1. $6x - 2 = 4x - 1$
Subtract $4x$ from both sides to collect $x$ terms.
$6x - 4x - 2 = -1$ $2x - 2 = -1$
Add 2 to both sides to isolate the $x$ term.
$2x = -1 + 2$ $2x = 1$
Divide by 2 to solve for $x$ .
$x = \frac{1}{2}$
The truth set is $\boxed{\left\{\frac{1}{2}\right\}}$ .
1. $3(2x+5) = 2(x-5) + 13$
Distribute the numbers on both sides of the equation.
$6x + 15 = 2x - 10 + 13$ $6x + 15 = 2x + 3$
Subtract $2x$ from both sides to collect $x$ terms.
$6x - 2x + 15 = 3$ $4x + 15 = 3$
Subtract 15 from both sides to isolate the $x$ term.
$4x = 3 - 15$ $4x = -12$
Divide by 4 to solve for $x$ .
$x = \frac{-12}{4}$ $x = -3$
The truth set is $\boxed{\{-3\}}$ .

Solve the following equations for x: 1) 6(3x-4) = -4(x+6) 2) 4 − 7x = 3x + 4 3) 6x − 2 = 4x − 1 4) 3(2x+5) = 2(x−5) + 13

Step-by-step solution

Distribute the numbers on both sides of the equation.

Add $4x$ to both sides to collect $x$ terms.

Add 24 to both sides to isolate the $x$ term.

Divide by 22 to solve for $x$ .

Add $7x$ to both sides to collect $x$ terms.

Subtract 4 from both sides to isolate the $x$ term.

Divide by 10 to solve for $x$ .

Subtract $4x$ from both sides to collect $x$ terms.

Add 2 to both sides to isolate the $x$ term.

Divide by 2 to solve for $x$ .

Distribute the numbers on both sides of the equation.

Subtract $2x$ from both sides to collect $x$ terms.

Subtract 15 from both sides to isolate the $x$ term.

Divide by 4 to solve for $x$ .

Still stuck on this one?

More Mathematics Questions

Solve the following equations for x: 1) 6(3x-4) = -4(x+6) 2) 4 − 7x = 3x + 4 3) 6x − 2 = 4x − 1 4) 3(2x+5) = 2(x−5) + 13

Step-by-step solution

Distribute the numbers on both sides of the equation.

Add 4x4x4x to both sides to collect xxx terms.

Add 24 to both sides to isolate the xxx term.

Divide by 22 to solve for xxx.

Add 7x7x7x to both sides to collect xxx terms.

Subtract 4 from both sides to isolate the xxx term.

Divide by 10 to solve for xxx.

Subtract 4x4x4x from both sides to collect xxx terms.

Add 2 to both sides to isolate the xxx term.

Divide by 2 to solve for xxx.

Distribute the numbers on both sides of the equation.

Subtract 2x2x2x from both sides to collect xxx terms.

Subtract 15 from both sides to isolate the xxx term.

Divide by 4 to solve for xxx.

Still stuck on this one?

More Mathematics Questions

Add $4x$ to both sides to collect $x$ terms.

Add 24 to both sides to isolate the $x$ term.

Divide by 22 to solve for $x$ .

Add $7x$ to both sides to collect $x$ terms.

Subtract 4 from both sides to isolate the $x$ term.

Divide by 10 to solve for $x$ .

Subtract $4x$ from both sides to collect $x$ terms.

Add 2 to both sides to isolate the $x$ term.

Divide by 2 to solve for $x$ .

Subtract $2x$ from both sides to collect $x$ terms.

Subtract 15 from both sides to isolate the $x$ term.

Divide by 4 to solve for $x$ .