All categories

3 years ago

Which of the following is(are) the solution(s( to |5x+2|=8?

Mathematics

2 answers:

olchik [2.2K]3 years ago

8 0

Since, this is an absolute value expression. We know that there is going to be 2 solutions.

We know that either 5x + 2 = 8 and 5x + 2 = -8 are the solutions.

Steps to solve:

5x + 2 = 8

~Subtract 2 to both sides

5x + 2 - 2 = 8 - 2

~Simplify

5x = 6

~Divide 5 to both sides

5x/5 = 6/5

~Simplify

x = 6/5

Steps to solve:

5x + 2 = -8

~Subtract 2 to both sides

5x + 2 - 2 = -8 - 2

~Simplify

5x = -10

~Divide 5 to both sides

5x/5 = -10/5

~Simplify

x = -2

Best of Luck!

larisa [96]3 years ago

7 0

Answer:

Step-by-step explanation:

Given that

|5x+2|=8

Note that

|x|=x for ×>0

|x|=-x for ×<0.

So, for the first case

|5x+2|=8

5x+2=8

5x=8-2

5x=6

x=6/5

Also, the second aspect.

|5x+2|=8

-(5x+2)=8

Divide both side by -

5x+2=-8

5x=-8-2

5x=-10

x=-10/2

x=-5

You might be interested in

Consider rolling two fair dice one 3-sided the other 5-sided

Ne4ueva [31]

Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

$1\leq x\leq 3,\quad 1\leq y \leq 5$

We have $P(X=x)=\frac{1}{3}$ and $P(Y=y)=\frac{1}{5}$ , because the dice are fair.

Now we use the assumption of independence to claim that

$P(X=x, Y=y) = P(X=x)\cdot P(Y=y) =\dfrac{1}{3}\cdot\dfrac{1}{5} = \dfrac{1}{15}$

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:

2 in a unique way (1+1)
3 in two possible ways (1+2, 2+1)
4 in three possible ways
5 in three possible ways
6 in three possible ways
7 in two possible ways
8 in a unique way

This implies that the probabilities of the outcomes of $W=X+Y$ are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5