Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-10}& = &-15 \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+10}& = &12 \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-12}& = &-10 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &-10\color{blue}{+12} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+8}& = &-2 \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8} & = &-2\color{blue}{-8} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-10}& = &14 \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &10x & = &24\\\Leftrightarrow & \color{red}{10}x & = &24\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{24}{10} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+12}& = &12 \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12} & = &12\color{blue}{-12} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-12}& = &-7 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12} & = &-7\color{blue}{+12} \\\Leftrightarrow &2x & = &5\\\Leftrightarrow & \color{red}{2}x & = &5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-6}& = &1 \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6} & = &1\color{blue}{+6} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+9}& = &-7 \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9} & = &-7\color{blue}{-9} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+5}& = &-15 \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5} & = &-15\color{blue}{-5} \\\Leftrightarrow &-4x & = &-20\\\Leftrightarrow & \color{red}{-4}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-20}{-4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+12}& = &8 \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12} & = &8\color{blue}{-12} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-1}& = &-5 \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)