Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{11})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{11}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{20}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-20} & = & \color{red}{33x} +6 \\\Leftrightarrow & 220x \color{red}{-20} \color{blue}{+20} \color{blue}{-33x} & = & \color{red}{33x} +6 \color{blue}{-33x} \color{blue}{+20} \\\Leftrightarrow & 220x-33x& = & 6+20 \\\Leftrightarrow & \color{red}{187} x& = & 26 \\\Leftrightarrow & x = \frac{26}{187} & & \\ & V = \left\{ \frac{26}{187} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+126} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -1848x \color{red}{+126} \color{blue}{-126} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-126} \\\Leftrightarrow & -1848x+539x& = & 110-126 \\\Leftrightarrow & \color{red}{-1309} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-1309} & & \\\Leftrightarrow & x = \frac{16}{1309} & & \\ & V = \left\{ \frac{16}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-90} & = & \color{red}{385x} +66 \\\Leftrightarrow & 1320x \color{red}{-90} \color{blue}{+90} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+90} \\\Leftrightarrow & 1320x-385x& = & 66+90 \\\Leftrightarrow & \color{red}{935} x& = & 156 \\\Leftrightarrow & x = \frac{156}{935} & & \\ & V = \left\{ \frac{156}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{3})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -14x-\frac{28}{3}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{-28} & = & \color{red}{-9x} +2 \\\Leftrightarrow & -42x \color{red}{-28} \color{blue}{+28} \color{blue}{+9x} & = & \color{red}{-9x} +2 \color{blue}{+9x} \color{blue}{+28} \\\Leftrightarrow & -42x+9x& = & 2+28 \\\Leftrightarrow & \color{red}{-33} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-33} & & \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{7})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{12}{7}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-12} & = & \color{red}{35x} +9 \\\Leftrightarrow & -84x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -84x-35x& = & 9+12 \\\Leftrightarrow & \color{red}{-119} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-119} & & \\\Leftrightarrow & x = \frac{-3}{17} & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & 7x+\frac{7}{11} \\\Leftrightarrow & 6x+\frac{6}{11}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+6} & = & \color{red}{77x} +7 \\\Leftrightarrow & 66x \color{red}{+6} \color{blue}{-6} \color{blue}{-77x} & = & \color{red}{77x} +7 \color{blue}{-77x} \color{blue}{-6} \\\Leftrightarrow & 66x-77x& = & 7-6 \\\Leftrightarrow & \color{red}{-11} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-11} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{8})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -10x-\frac{15}{8}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{-105} & = & \color{red}{-392x} +32 \\\Leftrightarrow & -560x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +32 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & -560x+392x& = & 32+105 \\\Leftrightarrow & \color{red}{-168} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-168} & & \\\Leftrightarrow & x = \frac{-137}{168} & & \\ & V = \left\{ \frac{-137}{168} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -20x-\frac{8}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{-16} & = & \color{red}{154x} +99 \\\Leftrightarrow & -440x \color{red}{-16} \color{blue}{+16} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{+16} \\\Leftrightarrow & -440x-154x& = & 99+16 \\\Leftrightarrow & \color{red}{-594} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-594} & & \\\Leftrightarrow & x = \frac{-115}{594} & & \\ & V = \left\{ \frac{-115}{594} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{15}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+45} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 210x \color{red}{+45} \color{blue}{-45} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-45} \\\Leftrightarrow & 210x+147x& = & 70-45 \\\Leftrightarrow & \color{red}{357} x& = & 25 \\\Leftrightarrow & x = \frac{25}{357} & & \\ & V = \left\{ \frac{25}{357} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{3})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{16}{3}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+16} & = & \color{red}{-27x} +10 \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+27x} & = & \color{red}{-27x} +10 \color{blue}{+27x} \color{blue}{-16} \\\Leftrightarrow & -24x+27x& = & 10-16 \\\Leftrightarrow & \color{red}{3} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{3} & & \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 35x+\frac{7}{3}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+7} & = & \color{red}{-24x} +2 \\\Leftrightarrow & 105x \color{red}{+7} \color{blue}{-7} \color{blue}{+24x} & = & \color{red}{-24x} +2 \color{blue}{+24x} \color{blue}{-7} \\\Leftrightarrow & 105x+24x& = & 2-7 \\\Leftrightarrow & \color{red}{129} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{129} & & \\ & V = \left\{ \frac{-5}{129} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -6x-\frac{8}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-80} & = & \color{red}{-490x} +49 \\\Leftrightarrow & -420x \color{red}{-80} \color{blue}{+80} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{+80} \\\Leftrightarrow & -420x+490x& = & 49+80 \\\Leftrightarrow & \color{red}{70} x& = & 129 \\\Leftrightarrow & x = \frac{129}{70} & & \\ & V = \left\{ \frac{129}{70} \right\} & \\\end{align}\)