Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+10}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10+11x } & = & -15 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &15x & = &-25\\\Leftrightarrow & \color{red}{15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+8}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-11x } & = & -6 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -6 \color{blue}{-8} \\\Leftrightarrow &-6x & = &-14\\\Leftrightarrow & \color{red}{-6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+3}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-5x } & = & -9 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-11}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-7x } & = & -3 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & -5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-11\\\Leftrightarrow & \color{red}{-16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+7}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-5x } & = & -13 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & 15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+14}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-11x } & = & -10 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &-18x & = &-24\\\Leftrightarrow & \color{red}{-18}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-24}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+2}& = & -14 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+3x } & = & -14 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+8}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-9x } & = & -14 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &2x & = &-22\\\Leftrightarrow & \color{red}{2}x & = &-22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-22}{2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)