Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for j
j∈(−∞,−42)∪(42,+∞)
Evaluate
j×j×8−15>−14
Multiply
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Evaluate
j×j×8
Multiply the terms
j2×8
Use the commutative property to reorder the terms
8j2
8j2−15>−14
Move the expression to the left side
8j2−15−(−14)>0
Subtract the numbers
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Evaluate
−15−(−14)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−15+14
Add the numbers
−1
8j2−1>0
Rewrite the expression
8j2−1=0
Move the constant to the right-hand side and change its sign
8j2=0+1
Removing 0 doesn't change the value,so remove it from the expression
8j2=1
Divide both sides
88j2=81
Divide the numbers
j2=81
Take the root of both sides of the equation and remember to use both positive and negative roots
j=±81
Simplify the expression
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Evaluate
81
To take a root of a fraction,take the root of the numerator and denominator separately
81
Simplify the radical expression
81
Simplify the radical expression
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Evaluate
8
Write the expression as a product where the root of one of the factors can be evaluated
4×2
Write the number in exponential form with the base of 2
22×2
The root of a product is equal to the product of the roots of each factor
22×2
Reduce the index of the radical and exponent with 2
22
221
Multiply by the Conjugate
22×22
Multiply the numbers
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Evaluate
22×2
When a square root of an expression is multiplied by itself,the result is that expression
2×2
Multiply the numbers
4
42
j=±42
Separate the equation into 2 possible cases
j=42j=−42
Determine the test intervals using the critical values
j<−42−42<j<42j>42
Choose a value form each interval
j1=−1j2=0j3=1
To determine if j<−42 is the solution to the inequality,test if the chosen value j=−1 satisfies the initial inequality
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Evaluate
8(−1)2−15>−14
Simplify
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Evaluate
8(−1)2−15
Evaluate the power
8×1−15
Any expression multiplied by 1 remains the same
8−15
Subtract the numbers
−7
−7>−14
Check the inequality
true
j<−42 is the solutionj2=0j3=1
To determine if −42<j<42 is the solution to the inequality,test if the chosen value j=0 satisfies the initial inequality
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Evaluate
8×02−15>−14
Simplify
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Evaluate
8×02−15
Calculate
8×0−15
Any expression multiplied by 0 equals 0
0−15
Removing 0 doesn't change the value,so remove it from the expression
−15
−15>−14
Check the inequality
false
j<−42 is the solution−42<j<42 is not a solutionj3=1
To determine if j>42 is the solution to the inequality,test if the chosen value j=1 satisfies the initial inequality
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Evaluate
8×12−15>−14
Simplify
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Evaluate
8×12−15
1 raised to any power equals to 1
8×1−15
Any expression multiplied by 1 remains the same
8−15
Subtract the numbers
−7
−7>−14
Check the inequality
true
j<−42 is the solution−42<j<42 is not a solutionj>42 is the solution
Solution
j∈(−∞,−42)∪(42,+∞)
Show Solution
