Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+14}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-7x } & = & -5 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+12}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-10x } & = & 8 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+7}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-9x } & = & -5 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+5}& = & -5 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+3x } & = & -5 \color{red}{ -3x }\color{blue}{-5+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-2}& = & -9 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+6x } & = & -9 \color{red}{ -6x }\color{blue}{+2+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & -8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-11}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-14x } & = & -3 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-27x & = &8\\\Leftrightarrow & \color{red}{-27}x & = &8\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{8}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{27} } & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-3}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-11x } & = & -5 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-9}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-7x } & = & 10 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-11}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & -2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+1}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+11x } & = & -7 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &26x & = &-8\\\Leftrightarrow & \color{red}{26}x & = &-8\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-8}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+9}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-7x } & = & -6 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)