Algebra does not have a very good reputation among students. While some find it mildly frustrating, many are convinced that it is a form of modern day torture. So given all the bad press surrounding it, it is natural that first time algebra learners might be a bit apprehensive about what to expect. Well the good news is that algebra is not the killer subject that many claim it is. And even better, getting a hang of this subject early on makes the advanced levels easier and possibly even interesting! Algebra 1 problem solver is an online tool that will help you master algebra quite easily. With a math problem solver algebra 1 help is available easily any time you want. Algebra 1 problem solvers offer a lot of advantages.

## Free Algebra 1 Problem Solver

### Solved Examples

**Question 1:**Solve the equation $\frac{2x}{ 3} + \frac{5}{7} = \frac{6x }{ 7}$ - 3

**Solution:**

Given $\frac{2x}{ 3} + \frac{5}{7} = \frac{6x }{ 7}$ - 3

The given equation has denominators that need to be cleared by multiplying all terms of the equation by the lowest common denominator.

LCD of the denominators 3 and 7 = 21

21($\frac{2x}{ 3} + \frac{5}{7}$) = 21($ \frac{6x }{ 7}$ - 3)

=> $\frac{2x * 21}{ 3} + \frac{5 * 21}{7}$ = $ \frac{6x * 21}{ 7 }$ - 3 * 21

=> 7 * 2x + 3 * 5 = 3 * 6x - 21 * 3

=> 14x + 15 = 18x - 63

Solve for x,

=> 4x = 78

Divide each side by 4

=> $\frac{4x}{4} = \frac{78}{4}$

=> x = 19 . 5

**Step 1:**The given equation has denominators that need to be cleared by multiplying all terms of the equation by the lowest common denominator.

LCD of the denominators 3 and 7 = 21

21($\frac{2x}{ 3} + \frac{5}{7}$) = 21($ \frac{6x }{ 7}$ - 3)

=> $\frac{2x * 21}{ 3} + \frac{5 * 21}{7}$ = $ \frac{6x * 21}{ 7 }$ - 3 * 21

=> 7 * 2x + 3 * 5 = 3 * 6x - 21 * 3

=> 14x + 15 = 18x - 63

**Step 2:**Solve for x,

**=> 18x - 14x = 63 + 15**

=> 4x = 78

Divide each side by 4

=> $\frac{4x}{4} = \frac{78}{4}$

=> x = 19 . 5

**answer****Question 2:**Factor the expression 10x

^{2}+ 20x - 80.

**Solution:**

Given 10x

Given polynomial is quadratic polynomial

Solve for x,

Factorized the polynomial

=> 10x

= 10x(x + 4) - 20(x + 4)

= (10x - 20)(x + 4)

=> 10x

^{2}+ 20x - 80Given polynomial is quadratic polynomial

Solve for x,

Factorized the polynomial

=> 10x

^{2}+ 20x - 80 = 10x^{2}+ 40x - 20x - 80= 10x(x + 4) - 20(x + 4)

= (10x - 20)(x + 4)

=> 10x

^{2}+ 20x - 80 = (10x - 20)(x + 4).**answer****Question 3:**The sum of two numbers is 70. One number is six less than the other number. Find the smaller number.

**Solution:**

Let the two numbers be x and y.

also y is smaller than x (y < x).

Given sum of two numbers is 70

=> x + y = 70 .......................................(1)

and one number is six less than the other number

=> y = x - 6 .........................................(2)

Solve equation (1) and equation (2)

Substitute equation (2) in (1)

=> x + (x - 6) = 70

=> x + x - 6 = 70

=> 2x - 6 = 70

Add 6 both sides

=> 2x - 6 + 6 = 70 + 6

=> 2x = 76

Divide each side by 2

=> $\frac{2x}{2} = \frac{76}{2}$

=> x = 38

Put x = 38 in equation (2)

=> y = 38 - 6

=> y = 32

Hence the smaller number is 32.

also y is smaller than x (y < x).

Step 1:Step 1:

Given sum of two numbers is 70

=> x + y = 70 .......................................(1)

and one number is six less than the other number

=> y = x - 6 .........................................(2)

**Step 2:**Solve equation (1) and equation (2)

Substitute equation (2) in (1)

=> x + (x - 6) = 70

=> x + x - 6 = 70

=> 2x - 6 = 70

Add 6 both sides

=> 2x - 6 + 6 = 70 + 6

=> 2x = 76

Divide each side by 2

=> $\frac{2x}{2} = \frac{76}{2}$

=> x = 38

**Step 3:**Put x = 38 in equation (2)

=> y = 38 - 6

=> y = 32

Hence the smaller number is 32.

**answer**