For questions 3 - 4, identify the symbol that correctly relates the two numbers, and then determine which number would be to the left of the other on a number line.
3. 17? 25 4. 42 ? 39

Goodluck

Step-by-step explanation:

9514 1404 393

  3. 17 < 25 . . . . 17 is on the left

  4. 42 > 39 . . . . 39 is on the left

Step-by-step explanation:

3. If you do any counting at all, you know that starting from 1, you reach the number 17 before you reach the number 25. That is 17 is less than 25.

The numbers increase to the right on the number line, so the relationship is ...

  17 < 25 . . . . . . . . 17 is to the left

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4. You can count to 39 sooner than you can count to 42.

  42 > 39 . . . . . . . . 39 is to the left

Additional comment

The point of the symbol (< or >) indicates the smaller value. The wider open end of the symbol indicates the larger value. One could say the symbol points to the number that is left on the number line.

Given a choice as to how to write an inequality, I often find it beneficial to write it so the "arrow" points to the left. That way, the written order of the operands corresponds to their relative locations on the number line.

For example, x < 3 means the number line will be shaded to the left of 3 to indicate possible values of x. 3 > x means the same thing, but requires more mental effort to figure out how to draw it on the number line.

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"Back in the day" we played games that required counting. Jump rope or hide-and-seek, for example. It became obvious that it took 10 times as long to count to 100 as to count to 10. That is, the place values of the digits in a number were quite clear, as was their order.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3