Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+11}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-10x } & = & 15 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-21\\\Leftrightarrow & \color{red}{-3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-21}{-3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-x } & = & -6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+9}& = & 3 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+14x } & = & 3 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &29x & = &-6\\\Leftrightarrow & \color{red}{29}x & = &-6\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-6}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{29} } & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-2}& = & -1 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2-2x } & = & -1 \color{red}{ +2x }\color{blue}{+2-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+12}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-13x } & = & -10 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-22\\\Leftrightarrow & \color{red}{-19}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-22}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-x } & = & 14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &5x & = &29\\\Leftrightarrow & \color{red}{5}x & = &29\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{29}{5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)