Question

solve the equations:
1.) 8x-3=7
2.) 5+7x=24
3.) 5=6+4x ​

Answer 1

Hi Student!

Usually the first step that I take for any problem would be to gather any important information that would be needed in the problem.  However, for this problem, it is pretty straight forward because we just need to solve for the unknown which is x.

Add 3 to both sides

• $8x - 3 = 7$

• $8x - 3 + 3 = 7 + 3$

• $8x = 10$

Divide 8 from both sides

• $\frac{8x}{8} = \frac{10}{8}$

• $x = \frac{10}{8}$

• $x = 1.25$

For the first equation, we were able to solve for x and get that the solution for the unknown is 1.25

Subtract 5 from both sides

• $5+7x=24$

• $5 - 5+7x=24- 5$

• $7x=19$

Divide both sides by 7

• $\frac{7x}{7}=\frac{19}{7}$

• $x=\frac{19}{7}$

For the second equation, we are able to solve for x and get that the solution for the unknown is 19/7

Subtract 6 from both sides

• $5=6+4x$

• $5-6=6-6+4x$

• $-1=4x$

Divide both sides by 4

• $\frac{-1}{4}=\frac{4x}{4}$

• $\frac{-1}{4}=x$

• $-0.25=x$

For the final equation, we are able to solve for x and get that the solution for the unknown is -0.25

Answer 2

Answer:

1) $x=\frac{5}{4}=1\frac{1}{4}$

2) $x=\frac{19}{7}=2\frac{5}{7}$

3) $x=-\frac{1}{4}$

Step-by-step explanation:

1) 8x - 3 = 7

1. Group all constants on the right side of the equation

$8x-3=7$

Add 3 to both sides:

$8x-3+3=7+3$

Simplify the arithmetic:

$8x=7+3$

Simplify the arithmetic:

$8x=10$

2. Isolate the x

$8x=10$

Divide both sides by 8:

$\frac{8x}{8}=\frac{10}{8}$

Simplify the fraction:

$x=\frac{10}{8}$

Find the greatest common factor of the numerator and denominator:

$x=\frac{5\cdot 2}{4\cdot 2}$

Factor out and cancel the greatest common factor:

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

2) 5 + 7x = 24

1. Group all constants on the right side of the equation.

$5+7x=24$

Subtract 5 from both sides:

$5+7x-5=24-5$

Group like terms:

$7x+5-5=24-5$

Simplify the arithmetic:

$7x=24-5$

Simplify the arithmetic:

$7x=19$

2. Isolate the x

$7x=19$

Divide both sides by 7:

$\frac{7x}{7}=\frac{19}{7}$

Simplify the fraction:

$x=\frac{19}{7}$

3)  5 = 6 + 4x

1. Swap sides

$5=6+4x$

Swap sides:

$6+4x=5$

2. Group all constants on the right side of the equation

$6+4x=5$

Subtract 6 from both sides:

$6+4x-6=5-6$

Group like terms:

$4x+6-6=5-6$

Simplify the arithmetic:

$4x=5-6$

Simplify the arithmetic:

$4x=-1$

3. Isolate the x

$4x=-1$

Divide both sides by 4:

$\frac{4x}{4}=\frac{-1}{4}$

Simplify the fraction:

$x=\frac{-1}{4}$

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Why learn this:

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

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Terms and topics

• Linear equations with one unknown

The most common use of linear equations is to solve problems involving an unknown variable, generally (but not always) x, and a known constant.

Solving linear equations requires isolating the unknown variable on one side of the equation and simplifying the remainder. Anything done to one side of the equation must also be done to the other when simplifying.

An equation of:

$ax+b=0$

A typical linear equation with one unknown is in which a and b are constants and x is the unknown variable. In this case, we would isolate x by removing b from both sides of the equation before solving for it. We'd then multiply both sides of the equation by a, yielding the following result:

$x = -\frac{b}{a}$

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