Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+7}& = &-4 \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7} & = &-4\color{blue}{-7} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+5}& = &-12 \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5} & = &-12\color{blue}{-5} \\\Leftrightarrow &8x & = &-17\\\Leftrightarrow & \color{red}{8}x & = &-17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-13}& = &4 \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13} & = &4\color{blue}{+13} \\\Leftrightarrow &9x & = &17\\\Leftrightarrow & \color{red}{9}x & = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+12}& = &-3 \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12} & = &-3\color{blue}{-12} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-4}& = &9 \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+7}& = &12 \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7} & = &12\color{blue}{-7} \\\Leftrightarrow &15x & = &5\\\Leftrightarrow & \color{red}{15}x & = &5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+11}& = &14 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &14\color{blue}{-11} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+6}& = &-6 \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6} & = &-6\color{blue}{-6} \\\Leftrightarrow &5x & = &-12\\\Leftrightarrow & \color{red}{5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+8}& = &14 \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8} & = &14\color{blue}{-8} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+15}& = &-6 \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15} & = &-6\color{blue}{-15} \\\Leftrightarrow &6x & = &-21\\\Leftrightarrow & \color{red}{6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+3}& = &-11 \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3} & = &-11\color{blue}{-3} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-10}& = &10 \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10} & = &10\color{blue}{+10} \\\Leftrightarrow &4x & = &20\\\Leftrightarrow & \color{red}{4}x & = &20\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{20}{4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)