Math  /  Algebra

Question3 Copy and complete these flow charts to work out the value of xx. a x1=5x1>5x=+1\begin{array}{l} x-1=5 \quad x \quad-1>5 \\ x=\square \quad \square+1 \end{array} cc x2=9x2>9x=+9\begin{array}{l} x-2=9 \quad x \quad-2>9 \\ x=\square \quad \square+\square 9 \end{array} e x10=8x10x=\begin{array}{l} x-10=8 \quad x \quad-10 \\ x=\square \square \square \end{array} b x3=8xx=x=+38x5=12x\begin{array}{ll} x-3=8 & x \\ x=\square & \square \\ x=+3 & 8 \\ x-5=12 & x \end{array} xx 12
4 Copy and complete these flow charts to work out the value of yy. a 2y=6y×26y=÷2÷26 b 4y=8y×4>8y=÷48\begin{array}{l} 2 y=6 \\ y \\ \times 2 \\ 6 \\ y=\square \square \div 2 \\ \div 2 \\ 6 \\ \text { b } 4 y=8 \\ y \\ \times 4>8 \\ y= \\ \div 4 \quad 8 \end{array}

Studdy Solution

STEP 1

What is this asking? We need to find the values of xx and yy by filling in the missing parts of these flow charts, showing our work at each step! Watch out! Don't rush!
It's easy to mix up adding and subtracting, or multiplying and dividing.
Make sure you're doing the *opposite* operation to move things around in the equations.

STEP 2

1. Solve for x in the first set of flow charts.
2. Solve for y in the second set of flow charts.

STEP 3

For *a*, we have x1=5x - 1 = 5.
To **isolate** xx, we need to **add** 1 to *both* sides of the equation.
This gives us x1+1=5+1x - 1 + 1 = 5 + 1, which simplifies to x=6x = \textbf{6}.

STEP 4

For *c*, we've got x2=9x - 2 = 9.
To get xx by itself, we **add** 2 to both sides: x2+2=9+2x - 2 + 2 = 9 + 2.
This simplifies to x=11x = \textbf{11}.

STEP 5

For *e*, we have x10=8x - 10 = 8.
We **add** 10 to both sides to **isolate** xx: x10+10=8+10x - 10 + 10 = 8 + 10, which means x=18x = \textbf{18}.

STEP 6

For *b*, we have x3=8x - 3 = 8.
We **add** 3 to both sides: x3+3=8+3x - 3 + 3 = 8 + 3, so x=11x = \textbf{11}.

STEP 7

Lastly, for the second part of *b*, x5=12x - 5 = 12. **Add** 5 to both sides to get xx alone: x5+5=12+5x - 5 + 5 = 12 + 5, which means x=17x = \textbf{17}.

STEP 8

For *a*, we have 2y=62y = 6.
To get yy by itself, we need to **divide** both sides by 2.
This looks like 2y2=62\frac{2y}{2} = \frac{6}{2}.
So, y=3y = \textbf{3}.

STEP 9

For *b*, we have 4y=84y = 8.
We **divide** both sides by 4 to **isolate** yy: 4y4=84\frac{4y}{4} = \frac{8}{4}.
Therefore, y=2y = \textbf{2}.

STEP 10

For the *x* equations: *a* x=6x = 6, *c* x=11x = 11, *e* x=18x = 18, *b* x=11x = 11 and x=17x = 17.
For the *y* equations: *a* y=3y = 3, *b* y=2y = 2.

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