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Pre Algebra
Section 4.4
Unit 4 - Equations
Section 4 – Solving Multi-Step Equations
If there is an x on both sides of the equal sign, we must find away to combine them by first getting them
on the same side of the equation.
Example 1) Solve
૛࢞ + ૠ = −૜࢞ + ૛૛
There is an x on both sides of the equal sign. The first step is to move them to the same side.
Step 1)
2‫ ݔ‬+ 7 = −3‫ ݔ‬+ 22
+3‫ݔ‬
+ 3‫ݔ‬
5‫ ݔ‬+ 7 = 0 + 22
To move the “- 3x” to the other side we do the
opposite and “+ 3x” to both sides.
5‫ ݔ‬+ 7 = 22
Step 2)
5‫ ݔ‬+ 7 = 22
−7 − 7
5‫ ݔ‬+ 0 = 15
To get rid of the “ + 7 “ we “ – 7 “ from both sides.
5‫ = ݔ‬15
Step 3)
5‫ = ݔ‬15
5
5
To get rid of the multiply by 5, we divide by 5 on both sides.
‫=ݔ‬3
The Solution is = 3 . As before we can plug is this solution for x in the original problem and we should
get a true statement.
Check: 2ሺ3ሻ + 7 = −3ሺ3ሻ + 22
6 + 7 = −9 + 22
13 = 13
American River College
185
Milano
Pre Algebra
Section 4.4
If you are working a problem with like terms that can be combined on the SAME SIDE of the equal sign,
it makes the problem significantly easier to begin by combining them.
Example 2)
૛࢞ + ૠ − ૟࢞ = ૠ࢞ − ૚ૢ + ૝
We need to combine like terms ON THE SAME SIDE of the “=” before doing anything else.
Step 1)
2‫ ݔ‬+ 7 − 6‫ = ݔ‬7‫ ݔ‬− 19 + 4
−4‫ ݔ‬+ 7 = 7‫ ݔ‬− 15
Combine like terms.
Step 2)
−4‫ ݔ‬+ 7 = 7‫ ݔ‬− 15
−7‫ݔ‬
− 7‫ݔ‬
−11‫ ݔ‬+ 7 = 0 − 15
Move the variable to one side.
−11‫ ݔ‬+ 7 = −15
Step 3)
−11‫ ݔ‬+ 7 = −15
−7 − 7
−11‫ ݔ‬+ 0 = −22
Get rid of the addition, then the multiplication.
−11‫ = ݔ‬−22
Step 4)
−11‫ = ݔ‬−22
−11
− 11
‫=ݔ‬2
The solution is ‫ = ݔ‬2. We can verify the solution by plugging 2 in for x in the original problem.
Check:
2ሺ2ሻ + 7 − 6ሺ2ሻ = 7ሺ2ሻ − 19 + 4
4 + 7 − 12 = 14 − 19 + 4
11 − 12 = −5 + 4
−1 = −1
American River College
186
Milano
Pre Algebra
Section 4.4
Sometimes it is necessary to distribute so you can simplify both sides of an equation.
Example 3)
૜ሺ૛࢞ − ૝ሻ + ૠ = ૞࢞ − ૚૞
Step 1)
3ሺ2‫ ݔ‬− 4ሻ + 7 = 5‫ ݔ‬− 15
6‫ ݔ‬− 12 + 7 = 5‫ ݔ‬− 15
Begin by distributing to drop the parentheses.
6‫ ݔ‬− 5 = 5‫ ݔ‬− 15
Combine like terms on the same side of the equal sign.
Step 2)
6‫ ݔ‬− 5 = 5‫ ݔ‬− 15
−5‫ݔ‬
− 5‫ݔ‬
‫ ݔ‬− 5 = 0 − 15
Move the x to the same side of the equal sign.
‫ ݔ‬− 5 = −15
Step 3)
‫ ݔ‬− 5 = −15
+5
+5
‫ ݔ‬+ 0 = −10
Move the – 5 by adding 5 to both sides.
‫ = ݔ‬−10
The Solution is ‫ = ݔ‬−10.
Check: 3ሺ2ሺ−10ሻ − 4ሻ + 7 = 5ሺ−10ሻ − 15
3ሺ−20 − 4ሻ + 7 = −50 − 15
3ሺ−24ሻ + 7 = −65
−72 + 7 = −65
−65 = −65
American River College
187
Milano
Pre Algebra
Section 4.4
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American River College
188
Milano
Pre Algebra
Section 4.4
Exercise 4.4
NAME:___________________________________
Solve the following.
1. 5‫ ݔ‬− 6 = −2‫ ݔ‬+ 15
2. 4‫ ݔ‬− 3 = 8‫ ݔ‬+ 9
4. 7‫ ݔ‬− 3‫ ݔ‬+ 2 = 5 − 2‫ ݔ‬+ 9
American River College
3. 4 − 3‫ = ݔ‬2‫ ݔ‬− 36
5. 6‫ ݔ‬− 3 + 2‫ = ݔ‬7‫ ݔ‬− ‫ ݔ‬+ 15
189
Milano
Pre Algebra
Section 4.4
6. −2‫ ݔ‬+ 7 − 12 + 3‫ = ݔ‬5‫ ݔ‬− 7‫ ݔ‬+ 10
7. 3ሺ‫ ݔ‬− 2ሻ + 7‫ = ݔ‬2ሺ‫ ݔ‬+ 3ሻ − 4
8. 5ሺ‫ ݔ‬− 3ሻ + 3 = 3‫ ݔ‬− ሺ4 + 2‫ݔ‬ሻ
9. 7‫ ݔ‬− 2ሺ‫ ݔ‬− 5ሻ = −3‫ ݔ‬+ 2ሺ‫ ݔ‬− 4ሻ
American River College
190
Milano