Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-7}& = &-13 \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+5}& = &-15 \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5} & = &-15\color{blue}{-5} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-8}& = &-4 \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-7}& = &-12 \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7} & = &-12\color{blue}{+7} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+7}& = &5 \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7} & = &5\color{blue}{-7} \\\Leftrightarrow &4x & = &-2\\\Leftrightarrow & \color{red}{4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+9}& = &-6 \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9} & = &-6\color{blue}{-9} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+7}& = &7 \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7} & = &7\color{blue}{-7} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-9}& = &-13 \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9} & = &-13\color{blue}{+9} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-11}& = &14 \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11} & = &14\color{blue}{+11} \\\Leftrightarrow &7x & = &25\\\Leftrightarrow & \color{red}{7}x & = &25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-7}& = &4 \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7} & = &4\color{blue}{+7} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-5}& = &-11 \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5} & = &-11\color{blue}{+5} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-3}& = &7 \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3} & = &7\color{blue}{+3} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)