Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-x } & = & -2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-11}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11-3x } & = & 1 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 1 \color{blue}{+11} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+12}& = & 14 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-10x } & = & 14 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & -13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+2}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-9x } & = & -12 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-14\\\Leftrightarrow & \color{red}{-17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-13}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-13x } & = & 7 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+8}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-14x } & = & 1 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)