What is -2|x-3|+1>=-5 ?

The solution to -2|x-3|+1>=-5 is 0<= x<= 6

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-2|x-3|+1>=-5

- 2 ∣ x - 3 ∣ + 1 \geq - 5

0 \leq x \leq 6

Interval Notation

[0, 6]

Solution steps

- 2 ∣ x - 3 ∣ + 1 \geq - 5

Move

1

to the right side

- 2 ∣ x - 3 ∣ \geq - 6

Multiply both sides by

- 1

2 ∣ x - 3 ∣ \leq 6

Divide both sides by

2

∣ x - 3 ∣ \leq 3

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3 \leq x - 3 \leq 3

x - 3 \geq - 3 and x - 3 \leq 3

x \geq 0 and x \leq 6

Merge Overlapping Intervals

0 \leq x \leq 6

7 - \frac{1}{4}

∣ 11 - 2 x ∣ - 6 > 11

\frac{6 4 ^{\frac{7}{10}}}{6 4 ^{\frac{1}{5}}}

\frac{a ^{2} - b ^{2}}{( b - a ) ^{2}}

(16)^{- \frac{3}{4}}