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kvasek [131]
3 years ago
15

Graph the solution on the number line |x-3| <5

Mathematics
1 answer:
Anettt [7]3 years ago
8 0

Answer:

-2<x<8

see below for graph

Step-by-step explanation:

First, we need to solve the inequality.

Inequality: |x-3|<5

Split into two equations:

x-3<5

x-3>-5 (notice how the sign is flipped when we make the number negative)

let's start with x-3<5

add 3 to both sides

x<8

now

x-3>-5

add 3 to both sides

x>-2

The graph is below

the intersection is the solution.

Notice how I made the maroon line go to the right- which shows that it's greater than (for x>-2) and the silver line go to the left, which shows that it's less than (for x<8)

the equation is -2<x<8

Hope this helps!

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The only error you made is on problem 3. Everything else is correct. Nice work.

-------------------------------------------------------

Here is how to solve problem 3

Plug x = 1 into the equation and solve for y

-3x + y = 1

-3*1 + y = 1 ... replace x with 1

-3 + y = 1

y - 3 = 1

y - 3 + 3 = 1 + 3 .... add 3 to both sides

y = 4

<h3>The answer is 4</h3>

-------------------------------------------------------

Verifying the answer:

Plug (x,y) = (1,4) into the equation. Both sides should be the same number after simplifying both sides.

-3x + y = 1

-3*1 + 4 = 1 ..... replace x with 1; replace y with 4

-3 + 4 = 1

1 = 1

The answer is confirmed.

If you were to graph -3x + y = 1, which is equivalent to y = 3x+1, you'll find that the point (1,4) is on this line.

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Each class briarwood elementary collect at least 54 of food during the drive. If there are 29 classes in the school,what was the
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<h2>1080+486=1566</h2>
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