Question

(31).
7x = 21 - x
+ x + x
8x = 21
x = 21/8
32.
4 - 20 = 16x
33.
16 - 9 = 16 - x
34.
4(x + 1) = 4 - 1
35.
7(a - 5) = 9 - 2
linear equation practice
36.
37.

1. x - 5/4 = 2.8
2. x/4 - x/6 = 1/4
3. n - 3/5 + 9/5 = 26

Explanation:

Step1: Solve 31: Isolate $x$

$7x = 21 - 4 \implies 7x=17 \implies x=\frac{17}{7}$

Step2: Solve 32: Isolate $x$

$4-20=16x \implies -16=16x \implies x=-1$

Step3: Solve 33: Isolate $z$

$10-9=4z-5 \implies 1=4z-5 \implies 4z=6 \implies z=\frac{3}{2}$

Step4: Solve 34: Simplify then isolate $z$

$4z+4=3 \implies 4z=-1 \implies z=-\frac{1}{4}$

Step5: Solve 35: Simplify then isolate $a$

$5a-25=a-2 \implies 4a=23 \implies a=\frac{23}{4}$

Step6: Solve 36: Isolate $n$

$\frac{10}{9}n=9+\frac{19}{9} \implies \frac{10}{9}n=\frac{81+19}{9} \implies 10n=100 \implies n=10$

Step7: Solve 37: Find common denominator

$\frac{1}{8}+\frac{5}{4}=\frac{1+10}{8}=\frac{11}{8}$ (Check: $\frac{11}{8}
eq\frac{10}{8}$, so this equation is false)

Step8: Solve 38: Isolate $x$

$x-2x=\frac{3}{11} \implies -x=\frac{3}{11} \implies x=-\frac{3}{11}$

Step9: Solve 39: Common denominator, isolate $x$

$\frac{3x-2x}{12}=\frac{1}{14} \implies \frac{x}{12}=\frac{1}{14} \implies x=\frac{12}{14}=\frac{6}{7}$

Step10: Solve 40: Simplify then isolate $a$

$a+\frac{6}{5}=26 \implies a=26-\frac{6}{5}=\frac{130-6}{5}=\frac{124}{5}$

Answer:

1. $x=\frac{17}{7}$
2. $x=-1$
3. $z=\frac{3}{2}$
4. $z=-\frac{1}{4}$
5. $a=\frac{23}{4}$
6. $n=10$
7. The equation is false (no solution)
8. $x=-\frac{3}{11}$
9. $x=\frac{6}{7}$
10. $a=\frac{124}{5}$