first invert fraction of the slope from 4/1 to 1/4 and switch sign. then figure out the y-intercept
the algebraic approach would work like this:
-4x + 10 = 1/4x + b
plug in what you got, here: the intersection information
-4*(4) + 10 = 1/4*(4) + b
-16 + 10 = 1 + b
-6 = 1 + b
-7 = b
answer is -1 < x < 5
-|x - 2|+ 9 > 6
Rearrange the terms
-|x - 2| > 6 - 9
-|x - 2| > - 3
then divide both sides of the inequality by the co- efficient of variable
|x - 2| < 3
convert the absolute inequality to standard inequality
-3 <x - 2 < 3
separate compound inequalities into system of inequality
{x - 2}> -3
{x - 2 < 3}
Rearrange variable to the left side of the equation
x > -3 + 2
calculate the sum or difference
x > -1
x -2 < 3
Rearrange variable to the left side of the equation
x < 3 + 2
calculate the sum or difference
x < 5
x > -1 and x < 5
Find intersection
-1 < x < 5
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
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The given angles are 95° and 135, and the value of x is 40.
<h3>What is the angle sum property?</h3>The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
The given angles are 95° and 135.
Let's consider the adjacent angle of 135 to be z.
So, as we can see that both angles make a linear pair.
z + 135 = 180
z = 180 - 135
z = 45
Let's consider the interior angle to be y.
then,
y = 95 ( vertically opposite angle)
Now, The angle sum property
x + y + z = 180
x = 180 - 95 + 45
x = 40
Thus, the value of x is 40.
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