Solve 5-2x > 4, then represent on a number line
1 answer:
Answer: x < 1/2 or x < 0.5
The graph is below
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There are two ways to solve this
Method 1
5 - 2x > 4
-2x > 4-5
-2x > -1
x < -1/(-2) .... note the inequality sign flips
x < 1/2
x < 0.5
The inequality sign flips whenever we divide both sides by a negative number.
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Method 2
5 - 2x > 4
5 - 2x+2x > 4+2x
5 > 4+2x
4+2x < 5
2x < 5-4
2x < 1
x < 1/2
x < 0.5
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To graph this on a number line, we'll plot an open hole at 1/2 or 0.5 on the number line. Then we shade to the left to represent all values smaller than 1/2 = 0.5
The open hole signals that 0.5 itself is NOT part of the solution set.
See the diagram below.
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The equation of a line that is perpendicular to the given line is y = –4x – 16.
Solution:
The equation of a line given is y = 0.25x – 7
Slope of the given line() = 0.25
Let be the slope of the perpendicular line.
Passes through the point (–6, 8).
<em>If two lines are perpendicular then the product of the slopes equal to –1.</em>
Point-slope intercept formula:
and
Substitute these in the formula, we get
Add 8 on both sides of the equation.
Hence the equation of a line that is perpendicular to the given line is
y = –4x – 16