To solve for $\displaystyle x$ in the equation

 $\displaystyle 6x = 15$

Divide both sides by the coefficient of $\displaystyle x$, which is $\displaystyle 6$.

$\displaystyle \frac{6x}{6} = \frac{15}{6}$

$\displaystyle x = 2\frac{1}{2}$

Convert fraction to decimal:

$\displaystyle x = 2.5$

To solve 

$\displaystyle \frac{23}{x} = 5$ 

$\displaystyle \frac{x}{1} (\frac{23}{x}) = \frac{x}{1} (\frac{5}{1})$

$\displaystyle 23 = 5x$

$\displaystyle \frac{23}{5} = x$

$\displaystyle 4\frac{3}{5} = x$

Convert to equivalent fraction with $\displaystyle 10$ as the denominator.

$\displaystyle 4\frac{3}{5} = 4\frac{6}{10}$

Convert to a decimal

$\displaystyle 4\frac{6}{10} = 4.6$

$\displaystyle x = 4.6$ is the correct answer.

To determine the product of $\displaystyle (x)(y)$, first solve each equation to get the values of those variables.

$\displaystyle 7x + 3 = 17$

Subtract $\displaystyle 3$ from both sides of the equation:

$\displaystyle 7x + 3 - 3 = 17-3$

$\displaystyle 7x = 14$

Divide both sides by the coefficient, which is$\displaystyle 7.$

$\displaystyle \frac{7x}{7} =\frac{14}{7}$

$\displaystyle x = 2$

$\displaystyle 2y-9 = -15$

Add $\displaystyle 9$ to both sides of the equation:

$\displaystyle 2y - 9 + 9 = -15 + 9$

$\displaystyle 2y = -6$

Divide both sides of the equation by the coefficient of the variable$\displaystyle y$, which is 2

$\displaystyle \frac{2y}{2} = \frac{-6}{2}$

$\displaystyle y = -3$

If $\displaystyle x = 2$ and  $\displaystyle y = -3$

 then the product of $\displaystyle (2) (-3) = -6$. 

$\displaystyle -6$ is the correct answer.

In order to find the solution, simply place the value of $\displaystyle y$, which is $\displaystyle 3$, in each equation.

$\displaystyle (6) (3) + 4 \neq 18$ 

$\displaystyle 2(3-2) \neq 6$

$\displaystyle 5 (3) - 9 \neq -6$

The only equation that is a true numerical statement if $\displaystyle y = 3$ is

$\displaystyle 4 (3+7) = 40$

Jaden already has $\displaystyle \$22$ of the $\displaystyle \$56.$ The variable would need to represent how much would be added to $\displaystyle $22$ to reach his goal of $\displaystyle $56.$   

Therefore, 

$\displaystyle \$22 + x = \$56$ is the equation that you would use to solve this word problem.

To solve, insert $\displaystyle -2$ for each $\displaystyle x$ variable in the equation.

$\displaystyle 2(-2^{3}) - 3(-2) + 7 =$

Using the Order of Operations, PEMDAS, solve the equation. PEMDAS stands for parentheses, exponents, multiplication/division, addition/subtraction. Remember the exponent tells you how many times to multiply the number by itself.

$\displaystyle -2^{3} = (-2) (-2) (-2) = -8$

The subtraction of a negative is the same as adding a positive.

$\displaystyle 2(-8) +6 + 7 =$

$\displaystyle -16 + 13 = -3$

To solve:

$\displaystyle 4 (x-3) = -23 + (3\times 5)$

First distribute the $\displaystyle 4$ to the terms inside the parentheses, and then solve using the Order of Operations or PEMDAS (Parentheses, Exponents. Multiplication/Division, Addition/Subtraction):

$\displaystyle 4x-12 = -23 + 15$ 

$\displaystyle 4x -12 = -8$

$\displaystyle 4x -12 + 12 = -8 + 12$

$\displaystyle 4x = 4$

$\displaystyle \frac{4x}{4} = \frac{4}{4}$

$\displaystyle x = 1$ is the correct answer.

Replace the variable $\displaystyle \small y$ with $\displaystyle \small 5$. Then solve using order of operation (PEMDAS).

$\displaystyle \small 2\left ( y-2\right )=6$

$\displaystyle \small 2\left ( 5-2\right )=6$

$\displaystyle \small 5-2=3$

$\displaystyle \small 2\times3=6$

To solve for x in this equation, we must get x to stand alone or get x by itself.  

In the equation

$\displaystyle 2x = 40$

to get x by itself, we must cancel out the 2 next to it.  To cancel it out, we will divide by 2.  If we divide on the left side, we must divide on the right.  So,

$\displaystyle \frac{2x}{2} = \frac{40}{2}$

$\displaystyle x = 20$

Therefore, after getting x to stand alone, we can see that $\displaystyle x=20$.

To solve for a, we want to get a to stand alone or be by itself.  To do that, in the equation

$\displaystyle a-5=2$

we need to cancel out the 5.  In this case, we are subtracting 5 on the left side.  To cancel it out, we need to add 5.  If we add 5 to the left side, we need to add 5 to the right side.  So we get

$\displaystyle a-5+5=2+5$

$\displaystyle a+0 = 7$

$\displaystyle a=7$

Therefore, if we solve for a in the equation, we get $\displaystyle a=7$.