Question

Solve with properstep step by step explaination
3x + 5 =0.5 - 7

0.1 ( t - 3) = 0.15 ( t - 4)

Answer 1

refer to the attachment.....

Answer 2

Answer:

1. $\large\boxed{x=-3.83}$

2. $\large\boxed{t=6}$

Step-by-step explanation:

To solve this problem, first you have to isolate by the x from one side of the equation. Addition property of equality is adding from both sides of an equation by the same number doesn't change the equation.

Given:

1.) 3x+5=0.5-7

First, subtract the numbers from left to right.

$\displaystyle 0.5-7=-6.5$

$\displaystyle 3x+5=-6.5$

Secondly, subtract 5 from both sides.

$\displaystyle 3x+5-5=-6.5-5$

Solution:

Solve.

$\displaystyle -6.5-5=-11.5$

$\displaystyle 3x=-11.5$

Then, divide by 3 from both sides.

$\displaystyle \frac{3x}{3}=\frac{-11.5}{3}$

Solve.

$\displaystyle -11.5\div3=\boxed{X=-3.83}$

So, the correct answer is x=-3.83.

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2.) 0.1(t-3)=0.15(t-4)

Given:

First, multiply 100 from both sides.

$\displaystyle 0.1(t-3)*100=0.15(t-4)*100$

Rewrite the problem down. (refine.)

$\displaystyle 10(t-3)=15(t-4)$

$\large\boxed{\textnormal{Distributive property}}$

$\displaystyle a(b+c)=ab+ac$

Expand the form solve with distributive property.

10(t-3)

A=10

B=T

C=3

10*t=10t

10*3=30

10t-30

15(t-4)

15*t=15t

15*4=60

15t-60

$\displaystyle 10t-30=15t-60$

Solution:

Next, add 30 from both sides.

$\displaystyle 10t-30+30=15t-60+30$

Solve.

$\displaystyle -60+30=30$

$\displaystyle 10t=15t-30$

Then, subtract 15t from both sides.

$\displaystyle 10t-15t=15t-30-15t$

Solve.

$\displaystyle 10-15=-5$

$\displaystyle -5t=-30$

Now, divide by -5 from both sides.

$\displaystyle \frac{-5t}{-5}=\frac{-30}{-5}$

Solve.

$\displaystyle -30\div-5=\boxed{6}$

Therefore, the correct answer is t=6.

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