Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+9}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-11x } & = & -9 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-6x & = &-18\\\Leftrightarrow & \color{red}{-6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-18}{-6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-9}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9+8x } & = & 6 \color{red}{ -8x }\color{blue}{+9+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-3}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+13x } & = & 8 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &20x & = &11\\\Leftrightarrow & \color{red}{20}x & = &11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-1}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-13x } & = & -1 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &-28x & = &0\\\Leftrightarrow & \color{red}{-28}x & = &0\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{0}{-28} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-x } & = & -14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-9}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+13x } & = & 13 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &21x & = &22\\\Leftrightarrow & \color{red}{21}x & = &22\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{22}{21} \\\Leftrightarrow & \color{green}{ x = \frac{22}{21} } & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-x } & = & 15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+2}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-9x } & = & 13 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+8}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+13x } & = & 2 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &21x & = &-6\\\Leftrightarrow & \color{red}{21}x & = &-6\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-6}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-x } & = & -12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &13x & = &-20\\\Leftrightarrow & \color{red}{13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+1}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-8x } & = & -10 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)