Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-7}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-9x } & = & -7 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & 3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-15}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+8x } & = & -3 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & 11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-4}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-13x } & = & 10 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-28x & = &14\\\Leftrightarrow & \color{red}{-28}x & = &14\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{14}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-7}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & 5 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-20x & = &12\\\Leftrightarrow & \color{red}{-20}x & = &12\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{12}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+7}& = & 11 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+2x } & = & 11 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+10}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10-11x } & = & -9 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+1}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-8x } & = & 3 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-8}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-7x } & = & -13 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+3}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-5x } & = & 5 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-13}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-x } & = & -5 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)