Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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