Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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