Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+10}& = &-6 \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10} & = &-6\color{blue}{-10} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-13}& = &13 \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13} & = &13\color{blue}{+13} \\\Leftrightarrow &4x & = &26\\\Leftrightarrow & \color{red}{4}x & = &26\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{26}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+7}& = &9 \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7} & = &9\color{blue}{-7} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+9}& = &-7 \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9} & = &-7\color{blue}{-9} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-5}& = &-12 \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-1}& = &-5 \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-2}& = &13 \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+10}& = &-15 \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10} & = &-15\color{blue}{-10} \\\Leftrightarrow &-8x & = &-25\\\Leftrightarrow & \color{red}{-8}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-25}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{25}{8} } & & \\ & V = \left\{ \frac{25}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-14}& = &-5 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &-5\color{blue}{+14} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+8}& = &-6 \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8} & = &-6\color{blue}{-8} \\\Leftrightarrow &12x & = &-14\\\Leftrightarrow & \color{red}{12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-14}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+2}& = &14 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2} & = &14\color{blue}{-2} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+8}& = &8 \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8} & = &8\color{blue}{-8} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)