Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-12x & = &22\\\Leftrightarrow & \color{red}{-12}x & = &22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+3}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-10x } & = & 12 \color{red}{ +10x }\color{blue}{-3-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-8}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+15x } & = & 10 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &19x & = &18\\\Leftrightarrow & \color{red}{19}x & = &18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-14}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-13x } & = & -1 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+14}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-13x } & = & 10 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-28x & = &-4\\\Leftrightarrow & \color{red}{-28}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-4}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & -6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+9}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-11x } & = & -11 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & 7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & 8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+14}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+12x } & = & 7 \color{red}{ -12x }\color{blue}{-14+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)