Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-105} & = & \color{red}{-196x} +16 \\\Leftrightarrow & -168x \color{red}{-105} \color{blue}{+105} \color{blue}{+196x} & = & \color{red}{-196x} +16 \color{blue}{+196x} \color{blue}{+105} \\\Leftrightarrow & -168x+196x& = & 16+105 \\\Leftrightarrow & \color{red}{28} x& = & 121 \\\Leftrightarrow & x = \frac{121}{28} & & \\ & V = \left\{ \frac{121}{28} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 20x-\frac{16}{3}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{48}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-48} & = & \color{red}{63x} +5 \\\Leftrightarrow & 180x \color{red}{-48} \color{blue}{+48} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{+48} \\\Leftrightarrow & 180x-63x& = & 5+48 \\\Leftrightarrow & \color{red}{117} x& = & 53 \\\Leftrightarrow & x = \frac{53}{117} & & \\ & V = \left\{ \frac{53}{117} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{9})& = & -5x+\frac{4}{9} \\\Leftrightarrow & -4x-\frac{4}{9}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{-4} & = & \color{red}{-45x} +4 \\\Leftrightarrow & -36x \color{red}{-4} \color{blue}{+4} \color{blue}{+45x} & = & \color{red}{-45x} +4 \color{blue}{+45x} \color{blue}{+4} \\\Leftrightarrow & -36x+45x& = & 4+4 \\\Leftrightarrow & \color{red}{9} x& = & 8 \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+66} & = & \color{red}{693x} +42 \\\Leftrightarrow & -616x \color{red}{+66} \color{blue}{-66} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-66} \\\Leftrightarrow & -616x-693x& = & 42-66 \\\Leftrightarrow & \color{red}{-1309} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-1309} & & \\\Leftrightarrow & x = \frac{24}{1309} & & \\ & V = \left\{ \frac{24}{1309} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{7})& = & 4x+\frac{9}{7} \\\Leftrightarrow & 15x-\frac{12}{7}& = & 4x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{-12} & = & \color{red}{28x} +9 \\\Leftrightarrow & 105x \color{red}{-12} \color{blue}{+12} \color{blue}{-28x} & = & \color{red}{28x} +9 \color{blue}{-28x} \color{blue}{+12} \\\Leftrightarrow & 105x-28x& = & 9+12 \\\Leftrightarrow & \color{red}{77} x& = & 21 \\\Leftrightarrow & x = \frac{21}{77} & & \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+96} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 528x \color{red}{+96} \color{blue}{-96} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-96} \\\Leftrightarrow & 528x+220x& = & 33-96 \\\Leftrightarrow & \color{red}{748} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{748} & & \\ & V = \left\{ \frac{-63}{748} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+32} & = & \color{red}{-126x} +49 \\\Leftrightarrow & -112x \color{red}{+32} \color{blue}{-32} \color{blue}{+126x} & = & \color{red}{-126x} +49 \color{blue}{+126x} \color{blue}{-32} \\\Leftrightarrow & -112x+126x& = & 49-32 \\\Leftrightarrow & \color{red}{14} x& = & 17 \\\Leftrightarrow & x = \frac{17}{14} & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-60} & = & \color{red}{-70x} +21 \\\Leftrightarrow & 168x \color{red}{-60} \color{blue}{+60} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{+60} \\\Leftrightarrow & 168x+70x& = & 21+60 \\\Leftrightarrow & \color{red}{238} x& = & 81 \\\Leftrightarrow & x = \frac{81}{238} & & \\ & V = \left\{ \frac{81}{238} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{3})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{16}{3}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+80} & = & \color{red}{45x} +18 \\\Leftrightarrow & -300x \color{red}{+80} \color{blue}{-80} \color{blue}{-45x} & = & \color{red}{45x} +18 \color{blue}{-45x} \color{blue}{-80} \\\Leftrightarrow & -300x-45x& = & 18-80 \\\Leftrightarrow & \color{red}{-345} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-345} & & \\\Leftrightarrow & x = \frac{62}{345} & & \\ & V = \left\{ \frac{62}{345} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 10x+\frac{10}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+70} & = & \color{red}{-539x} +66 \\\Leftrightarrow & 770x \color{red}{+70} \color{blue}{-70} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{-70} \\\Leftrightarrow & 770x+539x& = & 66-70 \\\Leftrightarrow & \color{red}{1309} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{1309} & & \\ & V = \left\{ \frac{-4}{1309} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{11})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{24}{11}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-120} & = & \color{red}{495x} +66 \\\Leftrightarrow & -990x \color{red}{-120} \color{blue}{+120} \color{blue}{-495x} & = & \color{red}{495x} +66 \color{blue}{-495x} \color{blue}{+120} \\\Leftrightarrow & -990x-495x& = & 66+120 \\\Leftrightarrow & \color{red}{-1485} x& = & 186 \\\Leftrightarrow & x = \frac{186}{-1485} & & \\\Leftrightarrow & x = \frac{-62}{495} & & \\ & V = \left\{ \frac{-62}{495} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 4x-\frac{6}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & 60x+105x& = & 10+18 \\\Leftrightarrow & \color{red}{165} x& = & 28 \\\Leftrightarrow & x = \frac{28}{165} & & \\ & V = \left\{ \frac{28}{165} \right\} & \\\end{align}\)