Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-8}& = &-8 \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8} & = &-8\color{blue}{+8} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-4}& = &5 \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4} & = &5\color{blue}{+4} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+3}& = &-11 \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3} & = &-11\color{blue}{-3} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-12}& = &7 \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12} & = &7\color{blue}{+12} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-2}& = &12 \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2} & = &12\color{blue}{+2} \\\Leftrightarrow &3x & = &14\\\Leftrightarrow & \color{red}{3}x & = &14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-8}& = &-15 \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8} & = &-15\color{blue}{+8} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-10}& = &4 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &4\color{blue}{+10} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-15}& = &-15 \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15} & = &-15\color{blue}{+15} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-7}& = &-2 \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7} & = &-2\color{blue}{+7} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-8}& = &-15 \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8} & = &-15\color{blue}{+8} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-7}& = &-6 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7} & = &-6\color{blue}{+7} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+13}& = &-4 \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13} & = &-4\color{blue}{-13} \\\Leftrightarrow &7x & = &-17\\\Leftrightarrow & \color{red}{7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)