Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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