Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-10}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-5x } & = & -14 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-6}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6+2x } & = & -1 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &17x & = &5\\\Leftrightarrow & \color{red}{17}x & = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-x } & = & -5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-12}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-7x } & = & -14 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-15\\\Leftrightarrow & \color{red}{-8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & 14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-7}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+2x } & = & -7 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & 4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-x } & = & -12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+4}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-7x } & = & 1 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+4}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-5x } & = & -1 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)