Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+6}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-4x } & = & -4 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+7}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-9x } & = & 7 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+15}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15-4x } & = & -10 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-25\\\Leftrightarrow & \color{red}{-3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-13}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-10x } & = & -5 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+5}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & -4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -4 \color{blue}{-5} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-10}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10+7x } & = & -3 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-8}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-7x } & = & -2 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-20x & = &6\\\Leftrightarrow & \color{red}{-20}x & = &6\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{6}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-5}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5-11x } & = & 14 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & 11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+6}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-7x } & = & 4 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)