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3 years ago

Solve the inequality |6x + 2| < 10 and graph its solution.

1 answer:

8 0

This is a modulus inequality.
First part: when (6x + 2) is positive
6x + 2 < 10
6x < 10 - 2
6x < 8
x < 8/6
x < 4/3

Second part: when (6x + 2) is negative.

-(6x + 2) < 10   Divide both sides of inequality by -1 and change the sign.

(6x + 2) > -10
   6x + 2 > -10
   6x > -10 - 2
   6x > -12 Divide both sides by 6.
   x > -12/6
   x > -2.

Combined solution:   x < 4/3 and x > -2

-2 < x < 4/3.

Graph is a line on the number line between -2 and 4/3.

-2 and 4/3 are excluded from solution.

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Please help?!

Anton [14]

Answer:

Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proof is below.

Step-by-step explanation:

Given:

In Δ PQT

PQ = 30 ft

QT = 28 ft

TP = 20 ft

In Δ QRS

QR = 15 ft

RS = 14 ft

SQ = 10 ft

To Prove:

Δ PQT ~ Δ QRS

Proof:

First we consider the ratio of the sides

$\frac{PQ}{QR}=\frac{30}{15} = \frac{2}{1}$ ..............( 1 )

$\frac{QT}{RS}=\frac{28}{14} = \frac{2}{1}$ ..............( 2 )

$\frac{TP}{SQ}=\frac{20}{10} = \frac{2}{1}$ ..............( 3 )

So By equation ( 1 ), ( 2 ) and ( 3 ) we get

$\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}$

Now in Δ PQT and Δ QRS we have

$\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}$

Which are corresponding sides of a similar triangle in proportion.

∴ Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proved

8 0

3 years ago

Ian earns £420 a week after a 5% rise. <br> What was his pay before?

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It turns out that 5% of 400 is 20.

(1/20)*400=20.

So Ian was being paid £400 a week before he was given a pay rise.

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Someone asked the same question here before, check it out

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