Answer: x < 3
Step-by-step explanation:
To solve this inequality, we will simplify and isolate the x variable.
Given:
5x - 4 < 2x + 5
Add 4 to both sides:
5x < 2x + 9
Subtract 2 from both sides:
3x< + 9
Divide both sides by 3:
x < 3
Step-by-step explanation:
Say you have these 2 fractions
Cross multiply as following;
If in the end, both numerator and denominator are equal, then the fractions are equivalent.
Examples:
Example 1
Cross multiply
They're equivalent.
Example 2
Cross multiply
They're not equivalent.
Step-by-step explanation:
Given the average of 8 numbers = 56.
Then the Total sum of 8 numbers = 56 * 8
= 448.
Sum of 1st three numbers = 49 + 57 + 72
= 178.
So, the total = 448 - 178
= 270.
Average of the other 5 numbers = 270/5
= 54.
Verification:
178 + 270 = 448/8
= 56.
Answer:
if 4 is 120° then 2 is also 180° since they are opposite angles.
1)
2x^2 - 13x - 24 = 0;
the discriminant is : ( - 13 )^2 - 4 * 2 * ( -24 ) = 169 + 192 = 361 = 19^2 => we have two different rational-number solutions ;
2)
[ -2( x + 2 ) - 3( x - 5 ) ] / [ ( x - 5 )( x + 2 ) ] < 0 <=>
( -5x + 11 ) / [ ( x - 5 )( x + 2 ) ] < 0
We have 2 situations :
a) - 5x + 11 < 0 and ( x - 5 )( x + 2 ) > 0 => x∈ ( 11 / 5 , + oo ) and x∈( -oo, - 2 )U
( 5 , + oo ) => x∈( 5, +oo);
b) - 5x + 11 > 0 and ( x - 5 )( x + 2 ) < 0 => x∈(-oo, 11/5) and x∈( -2, 5 ) =>
x∈( -2, 11/5 );
Finally, x∈ U (-2, 11 / 5 ) U ( 5, +oo).
