Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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