Answer:
D, (1,2)
Step-by-step explanation:
It all comes down to substitution. In this case the coefficient of x is 3 and the coefficient of y is 4. The format of these coordinates being (x,y).
1. Plug in your x value (1 in this circumstance) and solve:
3(1) + 4y < 12
3 + 4y < 12
2. Plug in your y value (2 in this circumstance) and solve:
3 + 4(2) < 12
3 + 8 < 12
3. Solve
3 + 8 = 11
11 < 12
Answer:
x<10
Step-by-step explanation:
Add '-7' to each side of the equation.
7 + -7 + -0.3x = 4 + -7
Combine like terms: 7 + -7 = 0
0 + -0.3x = 4 + -7
-0.3x = 4 + -7
Combine like terms: 4 + -7 = -3
-0.3x = -3
Divide each side by '-0.3'.
x = 10
Simplifying
x = 10
9514 1404 393
Answer:
(a) 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
Step-by-step explanation:
Replacement of -1/2(8x +2) by -4x -1 is use of the <em>distributive property</em>, eliminating choices B and D.
In step 3, addition of 1 to both sides of the equation is use of the <em>addition property of equality</em>, eliminating choice C. This leaves only choice A.
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<em>Additional comment</em>
This problem makes a distinction between the addition property of equality and the subtraction property of equality. They are essentially the same property, since addition of +1 is the same as subtraction of -1. The result shown in Step 3 could be from addition of +1 to both sides of the equation, or it could be from subtraction of -1 from both sides of the equation.
In general, you want to add the opposite of the number you don't want. Here, that number is -1, so we add +1. Of course, adding an opposite is the same as subtracting.
In short, you can argue both choices A and C have correct justifications. The only reason to prefer choice A is that we usually think of adding positive numbers as <em>addition</em>, and adding negative numbers as <em>subtraction</em>.
