The given equation is:
[tex]\displaystyle 7x-5=8(x+3)[/tex]
The first step you need to do is open the parentheses and distribute the 8 to x+3. It will be 8 times x and 3 times x.
[tex]8(x+3)=8 \times x+ 8 \times 3\\\\8 \times x=8x\\8 \times 3=24[/tex]
[tex]8(x+3) \rightarrow 8x+24[/tex]
Rewrite the equation:
[tex]7x-5=8x+24[/tex]
Now you need to move one of the variables to the other side.
If you move 7x to the other side, then:
You can move the variable by doing the opposite of it. Since 7x is positive, you can move it by subtracting 7x, which is negative. Subtract 7x on both sides:
[tex]7x-5-7x=8x+24-7x\\-5=x+24[/tex]
Now you need to leave x alone. x is being added to 24, so remove it by subtracting both sides by 24. Remember that when you're subtracting from a negative number, you're actually adding while keeping the negative sign.
[tex]-5-24=x+24-24[/tex]
Subtract:
[tex]\bf-29=x[/tex]
If you move 8x to the other side, then:
8x is positive, so you can move it by subtracting 8x, which is negative. Subtract 8x on both sides:
[tex]7x-5-8x=8x+24-8x\\-x-5=24[/tex]
You need to leave the variable alone, so move -5 to the other side. You can do this by adding 5 to both sides.
[tex]-x-5+5=24+5\\-x=29[/tex]
Lastly, x is negative, but you're looking for the value of positive x. Divide both sides by -1 to remove the negative sign.
[tex]\displaystyle \frac{-x}{-1} =\frac{29}{-1}[/tex]
Remember that a positive number divided by a negative number is negative. Divide:
[tex]\bf x=-29[/tex]
The answer to your question is x = -29.
