Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & 180x+63x& = & 30-8 \\\Leftrightarrow & \color{red}{243} x& = & 22 \\\Leftrightarrow & x = \frac{22}{243} & & \\ & V = \left\{ \frac{22}{243} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & -3x+\frac{7}{9} \\\Leftrightarrow & 4x+\frac{4}{9}& = & -3x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{+4} & = & \color{red}{-27x} +7 \\\Leftrightarrow & 36x \color{red}{+4} \color{blue}{-4} \color{blue}{+27x} & = & \color{red}{-27x} +7 \color{blue}{+27x} \color{blue}{-4} \\\Leftrightarrow & 36x+27x& = & 7-4 \\\Leftrightarrow & \color{red}{63} x& = & 3 \\\Leftrightarrow & x = \frac{3}{63} & & \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{-135x} +18 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-40} \\\Leftrightarrow & 120x+135x& = & 18-40 \\\Leftrightarrow & \color{red}{255} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{255} & & \\ & V = \left\{ \frac{-22}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{880}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 880x \color{red}{+165} & = & \color{red}{-396x} +24 \\\Leftrightarrow & 880x \color{red}{+165} \color{blue}{-165} \color{blue}{+396x} & = & \color{red}{-396x} +24 \color{blue}{+396x} \color{blue}{-165} \\\Leftrightarrow & 880x+396x& = & 24-165 \\\Leftrightarrow & \color{red}{1276} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{1276} & & \\ & V = \left\{ \frac{-141}{1276} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{11})& = & 4x+\frac{7}{2} \\\Leftrightarrow & -15x+\frac{15}{11}& = & 4x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x+ \frac{30}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{88x} +77 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-88x} & = & \color{red}{88x} +77 \color{blue}{-88x} \color{blue}{-30} \\\Leftrightarrow & -330x-88x& = & 77-30 \\\Leftrightarrow & \color{red}{-418} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-418} & & \\\Leftrightarrow & x = \frac{-47}{418} & & \\ & V = \left\{ \frac{-47}{418} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{7})& = & 2x+\frac{4}{9} \\\Leftrightarrow & 15x+\frac{20}{7}& = & 2x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+180} & = & \color{red}{126x} +28 \\\Leftrightarrow & 945x \color{red}{+180} \color{blue}{-180} \color{blue}{-126x} & = & \color{red}{126x} +28 \color{blue}{-126x} \color{blue}{-180} \\\Leftrightarrow & 945x-126x& = & 28-180 \\\Leftrightarrow & \color{red}{819} x& = & -152 \\\Leftrightarrow & x = \frac{-152}{819} & & \\ & V = \left\{ \frac{-152}{819} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 10x-\frac{4}{5}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{-8} & = & \color{red}{-90x} +25 \\\Leftrightarrow & 100x \color{red}{-8} \color{blue}{+8} \color{blue}{+90x} & = & \color{red}{-90x} +25 \color{blue}{+90x} \color{blue}{+8} \\\Leftrightarrow & 100x+90x& = & 25+8 \\\Leftrightarrow & \color{red}{190} x& = & 33 \\\Leftrightarrow & x = \frac{33}{190} & & \\ & V = \left\{ \frac{33}{190} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{+54} & = & \color{red}{-225x} +20 \\\Leftrightarrow & 270x \color{red}{+54} \color{blue}{-54} \color{blue}{+225x} & = & \color{red}{-225x} +20 \color{blue}{+225x} \color{blue}{-54} \\\Leftrightarrow & 270x+225x& = & 20-54 \\\Leftrightarrow & \color{red}{495} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{495} & & \\ & V = \left\{ \frac{-34}{495} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{6}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+42} & = & \color{red}{539x} +88 \\\Leftrightarrow & 1155x \color{red}{+42} \color{blue}{-42} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{-42} \\\Leftrightarrow & 1155x-539x& = & 88-42 \\\Leftrightarrow & \color{red}{616} x& = & 46 \\\Leftrightarrow & x = \frac{46}{616} & & \\\Leftrightarrow & x = \frac{23}{308} & & \\ & V = \left\{ \frac{23}{308} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{-14} & = & \color{red}{-6x} +2 \\\Leftrightarrow & 63x \color{red}{-14} \color{blue}{+14} \color{blue}{+6x} & = & \color{red}{-6x} +2 \color{blue}{+6x} \color{blue}{+14} \\\Leftrightarrow & 63x+6x& = & 2+14 \\\Leftrightarrow & \color{red}{69} x& = & 16 \\\Leftrightarrow & x = \frac{16}{69} & & \\ & V = \left\{ \frac{16}{69} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -4x+\frac{10}{3} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{-48x} +40 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{+48x} & = & \color{red}{-48x} +40 \color{blue}{+48x} \color{blue}{-45} \\\Leftrightarrow & -180x+48x& = & 40-45 \\\Leftrightarrow & \color{red}{-132} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-132} & & \\\Leftrightarrow & x = \frac{5}{132} & & \\ & V = \left\{ \frac{5}{132} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{9}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-27} & = & \color{red}{75x} +40 \\\Leftrightarrow & -180x \color{red}{-27} \color{blue}{+27} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+27} \\\Leftrightarrow & -180x-75x& = & 40+27 \\\Leftrightarrow & \color{red}{-255} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-255} & & \\\Leftrightarrow & x = \frac{-67}{255} & & \\ & V = \left\{ \frac{-67}{255} \right\} & \\\end{align}\)