Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-8}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-3x } & = & 10 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+4}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-7x } & = & 2 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+4}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+11x } & = & -9 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &14x & = &-13\\\Leftrightarrow & \color{red}{14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+4}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+6}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-5x } & = & -10 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+7}& = & -11 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+2x } & = & -11 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-1}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-4x } & = & -7 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-7}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-9x } & = & 2 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)