Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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