Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(-3x+7=-2\)
2. \(3x-2=-2\)
3. \(-3x+3=-13\)
4. \(-7x+8=-15\)
5. \(-7x-15=2\)
6. \(-8x-9=-6\)
7. \(9x+11=-14\)
8. \(-10x+5=-3\)
9. \(4x-11=-9\)
10. \(-8x-12=-12\)
11. \(-2x-15=6\)
12. \(12x-11=13\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+7}& = &-2 \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7} & = &-2\color{blue}{-7} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-2}& = &-2 \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+3}& = &-13 \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+8}& = &-15 \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8} & = &-15\color{blue}{-8} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-15}& = &2 \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15} & = &2\color{blue}{+15} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-9}& = &-6 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &-6\color{blue}{+9} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+11}& = &-14 \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &9x & = &-25\\\Leftrightarrow & \color{red}{9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+5}& = &-3 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &-3\color{blue}{-5} \\\Leftrightarrow &-10x & = &-8\\\Leftrightarrow & \color{red}{-10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-11}& = &-9 \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11} & = &-9\color{blue}{+11} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-12}& = &-12 \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12} & = &-12\color{blue}{+12} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-15}& = &6 \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15} & = &6\color{blue}{+15} \\\Leftrightarrow &-2x & = &21\\\Leftrightarrow & \color{red}{-2}x & = &21\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{21}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-11}& = &13 \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11} & = &13\color{blue}{+11} \\\Leftrightarrow &12x & = &24\\\Leftrightarrow & \color{red}{12}x & = &24\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{24}{12} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)