Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-2}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+6x } & = & -5 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+11}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-7x } & = & -8 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &2x & = &-19\\\Leftrightarrow & \color{red}{2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+13}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-9x } & = & -5 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &-x & = &-18\\\Leftrightarrow & \color{red}{-}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-18}{-1} \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-14}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-6x } & = & 13 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &7x & = &27\\\Leftrightarrow & \color{red}{7}x & = &27\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{27}{7} \\\Leftrightarrow & \color{green}{ x = \frac{27}{7} } & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x } & = & 2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-x } & = & 1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-10}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-13x } & = & -8 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x } & = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+12}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-10x } & = & 9 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & 8 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-11}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11+11x } & = & 15 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &23x & = &26\\\Leftrightarrow & \color{red}{23}x & = &26\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{26}{23} \\\Leftrightarrow & \color{green}{ x = \frac{26}{23} } & & \\ & V = \left\{ \frac{26}{23} \right\} & \\\end{align}\)