Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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