Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-10}& = &14 \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-10}& = &-1 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10} & = &-1\color{blue}{+10} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+10}& = &9 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &9\color{blue}{-10} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+10}& = &-7 \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10} & = &-7\color{blue}{-10} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-14}& = &-10 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &-10\color{blue}{+14} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+15}& = &15 \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15} & = &15\color{blue}{-15} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-7}& = &1 \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7} & = &1\color{blue}{+7} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-14}& = &-14 \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14} & = &-14\color{blue}{+14} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-10}& = &2 \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+11}& = &-5 \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-7}& = &15 \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7} & = &15\color{blue}{+7} \\\Leftrightarrow &14x & = &22\\\Leftrightarrow & \color{red}{14}x & = &22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-9}& = &-14 \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9} & = &-14\color{blue}{+9} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)