Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x } & = & -12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-24\\\Leftrightarrow & \color{red}{-14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+1}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+14x } & = & 11 \color{red}{ -14x }\color{blue}{-1+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+7}& = & 12 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+15x } & = & 12 \color{red}{ -15x }\color{blue}{-7+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+11}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-11x } & = & 14 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+11}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+2x } & = & 13 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & 1 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-15}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+13x } & = & 15 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &22x & = &30\\\Leftrightarrow & \color{red}{22}x & = &30\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{30}{22} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+15}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+6x } & = & 12 \color{red}{ -6x }\color{blue}{-15+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-11}& = & 14 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11+12x } & = & 14 \color{red}{ -12x }\color{blue}{+11+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &25x & = &25\\\Leftrightarrow & \color{red}{25}x & = &25\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{25}{25} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & 3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-11\\\Leftrightarrow & \color{red}{-14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)