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# Solve the inequality $4\left(x-1\right)^2\geq \left(2x-3\right)^2-7$

## Step-by-step Solution

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###  Solution

$x\geq -\frac{1}{2}$
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##  Step-by-step Solution 

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A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$

$4\left(x^2-2x+1\right)\geq \left(2x-3\right)^2-7$

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$4\left(x^2-2x+1\right)\geq \left(2x-3\right)^2-7$

Learn how to solve problems step by step online. Solve the inequality 4(x-1)^2>=(2x-3)^2-7. A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. Expand \left(2x-3\right)^2. Subtract the values 9 and -7. The power of a product is equal to the product of it's factors raised to the same power.

$x\geq -\frac{1}{2}$

SnapXam A2

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x
y
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(◻)
+
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◻/◻
/
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch