Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-6}& = &-13 \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6} & = &-13\color{blue}{+6} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-5}& = &9 \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5} & = &9\color{blue}{+5} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-15}& = &-8 \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15} & = &-8\color{blue}{+15} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+6}& = &15 \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-3}& = &-4 \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3} & = &-4\color{blue}{+3} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+1}& = &9 \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1} & = &9\color{blue}{-1} \\\Leftrightarrow &10x & = &8\\\Leftrightarrow & \color{red}{10}x & = &8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-8}& = &-6 \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8} & = &-6\color{blue}{+8} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-3}& = &12 \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &3x & = &15\\\Leftrightarrow & \color{red}{3}x & = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+15}& = &5 \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15} & = &5\color{blue}{-15} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-7}& = &5 \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-5}& = &12 \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5} & = &12\color{blue}{+5} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+11}& = &-9 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &-9\color{blue}{-11} \\\Leftrightarrow &-12x & = &-20\\\Leftrightarrow & \color{red}{-12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)