Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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