Question

3.2.4 how can i use my equation - solving skills? more solving equations to solve problems 3 - 92. for the following equations, solve for x. record your work and check your solution. a. $\frac{1}{2}x - 2=x - 4$ b. $8 - 0.25x = 0.5x+2$ c. $x + 2 - 0.5x=1 + 0.5x + 1$ d. $7x - 0.15=2x + 0.6$ e. $75c - 300=25c + 200$ f. $26y - 4 - 11y=15y + 6$ g. $-\frac{1}{3}x = 6$ h. $0.8 - 2t=1 - 3t$

Explanation:

Step1: Solve equation a

Isolate x terms. Subtract $\frac{1}{2}x$ from both sides:
$-2=x - \frac{1}{2}x-4$, then $-2=\frac{1}{2}x - 4$. Add 4 to both sides: $\frac{1}{2}x=2$, multiply both sides by 2, $x = 4$.

Step2: Solve equation b

Combine like - terms. Add $0.25x$ to both sides: $8=0.5x + 0.25x+2$, so $8 = 0.75x+2$. Subtract 2 from both sides: $0.75x=6$, divide both sides by $0.75$, $x = 8$.

Step3: Solve equation c

Simplify both sides first. The left - hand side is $x+2 - 0.5x=0.5x + 2$, and the right - hand side is $1 + 0.5x+1=0.5x + 2$. This is an identity, so $x$ can be any real number.

Step4: Solve equation d

Isolate x terms. Subtract $2x$ from both sides: $7x-2x-0.15=0.6$, so $5x=0.6 + 0.15$. Then $5x=0.75$, divide both sides by 5, $x = 0.15$.

Step5: Solve equation e

This equation is for c. Combine like - terms. Subtract $25c$ from both sides: $75c-25c-300=200$, so $50c=200 + 300$. Then $50c=500$, divide both sides by 50, $c = 10$.

Step6: Solve equation f

Combine like - terms on the left - hand side: $26y-11y-4=15y + 6$, so $15y-4=15y + 6$. Subtract $15y$ from both sides: $-4
eq6$, so there is no solution.

Step7: Solve equation g

Isolate x. Multiply both sides by - 2: $x=-12$.

Step8: Solve equation h

Isolate t terms. Add $3t$ to both sides: $0.8-2t + 3t=1$, so $0.8+t=1$. Subtract $0.8$ from both sides: $t=1 - 0.8$, $t = 0.2$.

Answer:

a. $x = 4$
b. $x = 8$
c. $x$ is any real number
d. $x = 0.15$
e. $c = 10$
f. No solution
g. $x=-12$
h. $t = 0.2$