Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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