could someone please check these problems for me? Thank you!
1. -0.7x<-35
x<50
2. Solve by elimination
3x+4y=3
6x+8y=6
answer:0
3. find y intercept to graph
x+5y=10
answer: (0,2)(10,0)
4. use distributive law to solve
7(w-5)=-35
7w-35=-35
if i add 35 to both sides i get 0
5. Simplify
1[-61-(58-85)]
1[-61-(-27)]
1[-61+27]
-61+27
-34
1. To solve the inequality -0.7x < -35, we want to isolate the variable x. The first step is to divide both sides of the inequality by -0.7. However, since we are dividing by a negative number, the inequality sign will flip. So we have:
x > -35 / -0.7
Simplifying, we get:
x > 50
Therefore, the solution to the inequality is x < 50.
2. To solve the system of equations using elimination, we want to eliminate one variable by performing operations on the equations. In this case, we can eliminate y by multiplying the first equation by 2 and the second equation by -1, so they have the same coefficient for y. The resulting equations are:
2(3x + 4y) = 2(3)
-1(6x + 8y) = -1(6)
Simplifying, we get:
6x + 8y = 6
-6x - 8y = -6
Adding these equations together, we eliminate y:
6x - 6x + 8y - 8y = 6 - 6
0 = 0
Since we end up with 0 = 0, this means that the two equations are equivalent and have infinitely many solutions. In other words, there are infinitely many values of x and y that satisfy the system of equations.
3. To find the y-intercept of the graph, we want to determine the point where the line intersects the y-axis. To do this, we need to set x = 0 in the equation x + 5y = 10 and solve for y:
0 + 5y = 10
Simplifying, we get:
5y = 10
y = 10 / 5
y = 2
Therefore, the y-intercept of the graph is (0, 2).
4. To solve the equation 7(w - 5) = -35 using the distributive law, we need to distribute the 7 to both terms inside the parentheses:
7w - 7(5) = -35
Simplifying, we get:
7w - 35 = -35
To solve for w, we can add 35 to both sides of the equation:
7w - 35 + 35 = -35 + 35
7w = 0
Therefore, the solution to the equation is w = 0.
5. To simplify the expression 1[-61 - (58 - 85)], we follow the order of operations (PEMDAS/BODMAS). First, we simplify the expression inside the innermost parentheses:
58 - 85 = -27
Now we substitute the simplified expression back into the original expression:
1[-61 - (-27)]
To remove the double negative, we change the subtraction of -27 to addition:
1[-61 + 27]
Simplifying further, we get:
1[-34]
Finally, multiplying 1 with -34, we obtain:
-34
Therefore, the simplified expression is -34.