Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+15}& = &-9 \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15} & = &-9\color{blue}{-15} \\\Leftrightarrow &-3x & = &-24\\\Leftrightarrow & \color{red}{-3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-24}{-3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+7}& = &8 \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7} & = &8\color{blue}{-7} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-2}& = &10 \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2} & = &10\color{blue}{+2} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+10}& = &-8 \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10} & = &-8\color{blue}{-10} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+13}& = &-2 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &-2\color{blue}{-13} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+7}& = &5 \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7} & = &5\color{blue}{-7} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+15}& = &15 \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15} & = &15\color{blue}{-15} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+11}& = &-2 \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11} & = &-2\color{blue}{-11} \\\Leftrightarrow &12x & = &-13\\\Leftrightarrow & \color{red}{12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-10}& = &13 \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10} & = &13\color{blue}{+10} \\\Leftrightarrow &7x & = &23\\\Leftrightarrow & \color{red}{7}x & = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+5}& = &6 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &6\color{blue}{-5} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+2}& = &-9 \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2} & = &-9\color{blue}{-2} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+1}& = &-9 \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)