SOLVING LINEAR EQUATIONS IN ONE VARIABLE PRACTICE SAT

Problem 1 :

Solution :

Doing cross multiplication, we get

2(x - 1) = 3(x + 1) 

2x - 2 = 3x + 3

2 x - 3x = 3 + 2

-x = 5

x = -5

Problem 2 :

a)  {0}   b) {0, 3}    c)  {1, 2}     d) {1, 3}

Solution :

Problem 3 :

8ax - 4 = 24

Based on the equation above, what is the value of 2ax - 1 ?

a)  3   b)  6    d)  8    d)  13

Solution :

Given that, 8ax - 4 = 24

Dividing by 4 on both sides,

2ax - 1 = 6

So, the value of 2ax - 1 is 6.

Problem 4 :

If 2x + 3 = x - 4, what is the value x + 8

a)  -7   b)  -1    c)  1   d)  7

Solution :

2x + 3 = x - 4

Subtracting x on both sides.

2x - x + 3 = -4

Subtracting 3 on both sides

x = -4 - 3

x = -7

So, the value of x is -7.

Problem 5 :

Solution :

8z = 20z - 21

8z - 20z = -21

-12z = -21

z = 21/12

z = 7/4

So, the value of z is 7/4.

Problem 6 :

9ax +  9b - 6 = 21

Based on the equation above, what is the value of ax + b ?

a) 3     b) 6     c) 8     d) 12

Solution :

9ax +  9b - 6 = 21

Adding 6 on both sides, we get

9ax + 9b = 21 + 6

9ax + 9b = 27

Dividing by 9 , we get

ax + b = 27/9

ax + b = 3

So, the value of ax+b is 3.

Problem 7 :

What is the value of t ?

a)  45/11   b)  5    c)  11/2    d)  55/9

Solution :

(t + 5) / (t - 5) = 10

Multiplying by t - 5 on both sides, we get

t + 5 = 10(t - 5)

t + 5 = 10t - 50

t - 10t = -50 - 5

-9t = -55

Dividing by 9 on both sides.

t = 55/9

So, the value of t is 55/9.

Problem 8 :

Last week Raul worked 11 more hours than Angelica. If they worked a combined total of 59 hours, how many hours did Angelica work last week?

a) 24     b) 35     c) 40     d) 48

Solution :

Let x be the number of hours Angelica works'

Number of hours Rahul works = x + 11

Altogether they work for 59 hours

x + x + 11 = 59

2x + 11 = 59

2x = 59 - 11

2x = 48

x = 48/2

x = 24

So, the number of hours Angelica works is 24.

Problem 9 :

The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true?

a) 30 = 2 x    b) 2 = 30 x     c) x/2 = 30     d) x + 30 = 2

Solution :

x states joined between 1850 and 1900 

Number of states joined in between 1776 and 1849 = 2x

30 = 2x

So, the answer is option a.

Problem 10 :

What is the value of x/5 ?

a)  10   b)  5   c)  2   d) 1/2

Solution :

5/x = 15/(x + 20)

Doing cross multiplication, we get

5(x +20) = 15x

5x + 100 = 15x

Subtracting 15x and 100 on both sides

5x - 15x = -100

-10x = -100

Dividing by 10 on both sides.

x = 100/10

x = 10

The value of x is 10.

Problem 11 :

Solution :

Problem 12 :

At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

Solution :

Let x be the number of calories in each order of fries.

Number of calories in Hamburgers = x + 50

2(x + 50) + 3x = 1700

2x + 100 + 3x = 1700

5x + 100 = 1700

5x = 1700 - 100

5x = 1600

Dividing by 5 on both sides.

x = 1600/5

x = 320

Number of calories Hamburgers have = x + 50

= 320 + 50

= 370