Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+12}& = &5 \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12} & = &5\color{blue}{-12} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+7}& = &-7 \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7} & = &-7\color{blue}{-7} \\\Leftrightarrow &8x & = &-14\\\Leftrightarrow & \color{red}{8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+4}& = &-6 \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4} & = &-6\color{blue}{-4} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-12}& = &15 \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &-14x & = &27\\\Leftrightarrow & \color{red}{-14}x & = &27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{14} } & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+4}& = &-7 \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-10}& = &2 \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+13}& = &-4 \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13} & = &-4\color{blue}{-13} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+5}& = &-11 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &-11\color{blue}{-5} \\\Leftrightarrow &-10x & = &-16\\\Leftrightarrow & \color{red}{-10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+1}& = &-15 \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &14x & = &-16\\\Leftrightarrow & \color{red}{14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-8}& = &-11 \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8} & = &-11\color{blue}{+8} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-4}& = &9 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+14}& = &-2 \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)