Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+11}& = & -12 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-8x } & = & -12 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-23\\\Leftrightarrow & \color{red}{-15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{23}{15} } & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & -5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & -2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+12}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+15x } & = & -14 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &19x & = &-26\\\Leftrightarrow & \color{red}{19}x & = &-26\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-26}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{19} } & & \\ & V = \left\{ \frac{-26}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-5}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-5x } & = & 6 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &4x & = &11\\\Leftrightarrow & \color{red}{4}x & = &11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-6}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-7x } & = & -10 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-x } & = & 8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &6x & = &-6\\\Leftrightarrow & \color{red}{6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-6}{6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-2}& = & -14 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-2x } & = & -14 \color{red}{ +2x }\color{blue}{+2-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & 2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & -12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-24\\\Leftrightarrow & \color{red}{-6}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-24}{-6} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-13}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-10x } & = & 3 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &3x & = &16\\\Leftrightarrow & \color{red}{3}x & = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)