Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & -6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -6 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-x } & = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-14}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14+7x } & = & -3 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &8x & = &11\\\Leftrightarrow & \color{red}{8}x & = &11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &9x & = &-7\\\Leftrightarrow & \color{red}{9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+7}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+4x } & = & 14 \color{red}{ -4x }\color{blue}{-7+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-9}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-7x } & = & 10 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-20x & = &19\\\Leftrightarrow & \color{red}{-20}x & = &19\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{19}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{20} } & & \\ & V = \left\{ \frac{-19}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-14}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-7x } & = & -15 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &-20x & = &-1\\\Leftrightarrow & \color{red}{-20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+4}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-5x } & = & -4 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-1}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-8x } & = & 11 \color{red}{ +8x }\color{blue}{+1-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-21x & = &12\\\Leftrightarrow & \color{red}{-21}x & = &12\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{12}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-x } & = & 4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-3}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3-8x } & = & -5 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+11}& = & -1 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-2x } & = & -1 \color{red}{ +2x }\color{blue}{-11-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)