Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & 12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-1}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-7x } & = & 7 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-17x & = &8\\\Leftrightarrow & \color{red}{-17}x & = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-2}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-5x } & = & 12 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-7}& = & -12 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-8x } & = & -12 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-15}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15+7x } & = & -6 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-x } & = & -5 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+2}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2+9x } & = & -12 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &23x & = &-14\\\Leftrightarrow & \color{red}{23}x & = &-14\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-14}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{23} } & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & -7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)