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Section 1 – 3<br />
Solving Equations<br />
Solve each equation for the indicated variable.<br />
Example:<br />
ax − b<br />
= x + 2b;<br />
for x<br />
2<br />
⎛⎛ ax − b ⎞⎞<br />
2⎜⎜<br />
⎟⎟ = 2<br />
⎝⎝ 2 ⎠⎠<br />
ax − b = 2x<br />
+ 4b<br />
ax − 2x<br />
= 4b<br />
+ b<br />
ax − 2x<br />
= 5b<br />
x(<br />
a − 2) = 5b<br />
5b<br />
x =<br />
a − 2<br />
( x + 2b)<br />
multiply each sideby 2.<br />
simplify<br />
add and subtract.<br />
Moveall terms with an xtoone side and<br />
terms without an xtotheother side.<br />
Simplify<br />
Factor toisolatethe x.<br />
Divideeach sideby a − 2.<br />
1. 3m – n = 2m + n ; for m 2. 2(u + 3v) = w – 5u ; for u<br />
1<br />
2 5<br />
3. r + 3s<br />
= 1 ; for r 4. f + g = 1−<br />
fg;<br />
for f<br />
2<br />
3 12<br />
x + k 3<br />
5. = ; for x<br />
j 4<br />
x + 3 2<br />
6. = t ; for x<br />
t<br />
Solve each equation.<br />
1<br />
2<br />
⎛⎛ 3 ⎞⎞<br />
− ⎜⎜ ⎟⎟<br />
8. 1.2(x + 5) = 1.6(2x + 5)<br />
⎝⎝ 2 ⎠⎠<br />
7. ( x 3) + − x = 5x<br />
4 ⎞⎞<br />
9. 3 ⎜⎜<br />
⎛⎛ u u u<br />
t − t + ⎟⎟ = 2 t + 3<br />
10. + − = 1<br />
⎝⎝ 3 ⎠⎠<br />
5 10 6<br />
Mrs. Beck & Mrs. Reynolds <br />
<strong>Honors</strong> <strong>Algebra</strong> 2 summer packet <br />
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