Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+7}& = &-15 \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7} & = &-15\color{blue}{-7} \\\Leftrightarrow &14x & = &-22\\\Leftrightarrow & \color{red}{14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+15}& = &-13 \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15} & = &-13\color{blue}{-15} \\\Leftrightarrow &-12x & = &-28\\\Leftrightarrow & \color{red}{-12}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-28}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+4}& = &-12 \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4} & = &-12\color{blue}{-4} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+11}& = &5 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+1}& = &-9 \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &11x & = &-10\\\Leftrightarrow & \color{red}{11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-15}& = &13 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15} & = &13\color{blue}{+15} \\\Leftrightarrow &4x & = &28\\\Leftrightarrow & \color{red}{4}x & = &28\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{28}{4} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-2}& = &13 \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &-13x & = &15\\\Leftrightarrow & \color{red}{-13}x & = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-11}& = &-7 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &-7\color{blue}{+11} \\\Leftrightarrow &2x & = &4\\\Leftrightarrow & \color{red}{2}x & = &4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{4}{2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-3}& = &-2 \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3} & = &-2\color{blue}{+3} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+3}& = &-13 \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-5}& = &-5 \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5} & = &-5\color{blue}{+5} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+2}& = &-7 \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2} & = &-7\color{blue}{-2} \\\Leftrightarrow &9x & = &-9\\\Leftrightarrow & \color{red}{9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-9}{9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)