Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+2}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+13x } & = & -11 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &22x & = &-13\\\Leftrightarrow & \color{red}{22}x & = &-13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{22} } & & \\ & V = \left\{ \frac{-13}{22} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+15}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-7x } & = & -12 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-27\\\Leftrightarrow & \color{red}{-16}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-27}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{27}{16} } & & \\ & V = \left\{ \frac{27}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-x } & = & 6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-9x & = &24\\\Leftrightarrow & \color{red}{-9}x & = &24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+1}& = & 3 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+4x } & = & 3 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & -3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-17\\\Leftrightarrow & \color{red}{-16}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-9}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+5x } & = & 11 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &13x & = &20\\\Leftrightarrow & \color{red}{13}x & = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &10x & = &-26\\\Leftrightarrow & \color{red}{10}x & = &-26\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-26}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-3}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3-7x } & = & 12 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)