Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-8}& = &13 \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8} & = &13\color{blue}{+8} \\\Leftrightarrow &-10x & = &21\\\Leftrightarrow & \color{red}{-10}x & = &21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+4}& = &-11 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &-11\color{blue}{-4} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-4}& = &-11 \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4} & = &-11\color{blue}{+4} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-7}& = &14 \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7} & = &14\color{blue}{+7} \\\Leftrightarrow &-15x & = &21\\\Leftrightarrow & \color{red}{-15}x & = &21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+13}& = &-13 \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13} & = &-13\color{blue}{-13} \\\Leftrightarrow &12x & = &-26\\\Leftrightarrow & \color{red}{12}x & = &-26\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-26}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-6}& = &-3 \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6} & = &-3\color{blue}{+6} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-10}& = &-10 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &-10\color{blue}{+10} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-9}& = &10 \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9} & = &10\color{blue}{+9} \\\Leftrightarrow &4x & = &19\\\Leftrightarrow & \color{red}{4}x & = &19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+8}& = &-3 \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8} & = &-3\color{blue}{-8} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+13}& = &-4 \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13} & = &-4\color{blue}{-13} \\\Leftrightarrow &10x & = &-17\\\Leftrightarrow & \color{red}{10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-17}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+6}& = &9 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &9\color{blue}{-6} \\\Leftrightarrow &15x & = &3\\\Leftrightarrow & \color{red}{15}x & = &3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+1}& = &14 \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1} & = &14\color{blue}{-1} \\\Leftrightarrow &6x & = &13\\\Leftrightarrow & \color{red}{6}x & = &13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)