Answer:
These are correct! Nice Job!!
Step-by-step explanation:
9514 1404 393
Answer:
- x ≤ 4
- x > 10
- x ≤ -7
Step-by-step explanation:
We're guessing you want to solve for x in each case. You do this in basically the same way you would solve an equation.
1. 3x +2 ≤ 14
3x ≤ 12 . . . . . subtract 2
x ≤ 4 . . . . . . . divide by 3
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2. -5 +2x > 15
2x > 20 . . . . . . add 5
x > 10 . . . . . . . . divide by 2
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3. -2x +4 ≥ 18
4 ≥ 18 +2x . . . . . add 2x
-14 ≥ 2x . . . . . . . subtract 18
-7 ≥ x . . . . . . . . . divide by 2
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<em>Additional comment</em>
The statement above that the same methods for solving apply to both equations and inequalities has an exception. The exception is that some operations reverse the order of numbers, so make the inequality symbol reverse. The usual operations we're concerned with are <em>multiplication and division by a negative number</em>: -2 < -1; 2 > 1, for example. There are other such operations, but they tend to be used more rarely for inequalities.
You will note that we avoided division by -2 in the solution of the third inequality by adding 2x to both sides, effectively giving the variable term a positive coefficient. You will notice that also changes its relation to the inequality symbol, just as if we had left the term where it was and reversed the symbol: -2x ≥ 14 ⇔ -14 ≥ 2x ⇔ x ≤ -7 ⇔ -7 ≥ x
Answer:
The linear relationship is represented by y = 2x + 3.
Step-by-step explanation:
We are given a y-intercept of an equation as well as a slope:
We can use this information and substitute it into the slope-intercept form equation to get our linear relationship:
In this formula, m is our slope and b is our y-intercept.
Therefore:
Finally, let us substitute these into the equation:
This is our final equation.
