Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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