Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & 13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-5x & = &21\\\Leftrightarrow & \color{red}{-5}x & = &21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & 13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+12}& = & -2 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-2x } & = & -2 \color{red}{ +2x }\color{blue}{-12-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &7x & = &-14\\\Leftrightarrow & \color{red}{7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-14}{7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & 9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & -15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & 6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+13}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-11x } & = & 15 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+12}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12+2x } & = & -8 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-15}& = & -4 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-2x } & = & -4 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+1}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-11x } & = & 8 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &4x & = &7\\\Leftrightarrow & \color{red}{4}x & = &7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+2}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+13x } & = & -10 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &23x & = &-12\\\Leftrightarrow & \color{red}{23}x & = &-12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{23} } & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)