Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & 8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-4}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+2x } & = & 8 \color{red}{ -2x }\color{blue}{+4+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+14}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14+7x } & = & -10 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &8x & = &-24\\\Leftrightarrow & \color{red}{8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-24}{8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-x } & = & -10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-25\\\Leftrightarrow & \color{red}{-16}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-5}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+2x } & = & 14 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-11}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+13x } & = & 3 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &21x & = &14\\\Leftrightarrow & \color{red}{21}x & = &14\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{14}{21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+3}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-7x } & = & -5 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-12}& = & -14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12+4x } & = & -14 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & 6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+12}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-10x } & = & 10 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-2\\\Leftrightarrow & \color{red}{-19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+7}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7-5x } & = & 4 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)