Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 20x-\frac{20}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{180}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-180} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 1980x \color{red}{-180} \color{blue}{+180} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+180} \\\Leftrightarrow & 1980x+693x& = & 110+180 \\\Leftrightarrow & \color{red}{2673} x& = & 290 \\\Leftrightarrow & x = \frac{290}{2673} & & \\ & V = \left\{ \frac{290}{2673} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{+108} & = & \color{red}{315x} +40 \\\Leftrightarrow & 675x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & 675x-315x& = & 40-108 \\\Leftrightarrow & \color{red}{360} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{360} & & \\\Leftrightarrow & x = \frac{-17}{90} & & \\ & V = \left\{ \frac{-17}{90} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{9})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{14}{9}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x- \frac{70}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{-70} & = & \color{red}{-90x} +54 \\\Leftrightarrow & 945x \color{red}{-70} \color{blue}{+70} \color{blue}{+90x} & = & \color{red}{-90x} +54 \color{blue}{+90x} \color{blue}{+70} \\\Leftrightarrow & 945x+90x& = & 54+70 \\\Leftrightarrow & \color{red}{1035} x& = & 124 \\\Leftrightarrow & x = \frac{124}{1035} & & \\ & V = \left\{ \frac{124}{1035} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+40} & = & \color{red}{315x} +36 \\\Leftrightarrow & -270x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +36 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & -270x-315x& = & 36-40 \\\Leftrightarrow & \color{red}{-585} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-585} & & \\\Leftrightarrow & x = \frac{4}{585} & & \\ & V = \left\{ \frac{4}{585} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{7})& = & 9x+\frac{5}{3} \\\Leftrightarrow & -8x-\frac{4}{7}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{12}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-12} & = & \color{red}{189x} +35 \\\Leftrightarrow & -168x \color{red}{-12} \color{blue}{+12} \color{blue}{-189x} & = & \color{red}{189x} +35 \color{blue}{-189x} \color{blue}{+12} \\\Leftrightarrow & -168x-189x& = & 35+12 \\\Leftrightarrow & \color{red}{-357} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-357} & & \\\Leftrightarrow & x = \frac{-47}{357} & & \\ & V = \left\{ \frac{-47}{357} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+28} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -140x \color{red}{+28} \color{blue}{-28} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{-28} \\\Leftrightarrow & -140x+175x& = & 15-28 \\\Leftrightarrow & \color{red}{35} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{35} & & \\ & V = \left\{ \frac{-13}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -9x+\frac{5}{3} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-189x} +35 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+189x} & = & \color{red}{-189x} +35 \color{blue}{+189x} \color{blue}{-30} \\\Leftrightarrow & 525x+189x& = & 35-30 \\\Leftrightarrow & \color{red}{714} x& = & 5 \\\Leftrightarrow & x = \frac{5}{714} & & \\ & V = \left\{ \frac{5}{714} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{-385x} +70 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & 1848x+385x& = & 70+330 \\\Leftrightarrow & \color{red}{2233} x& = & 400 \\\Leftrightarrow & x = \frac{400}{2233} & & \\ & V = \left\{ \frac{400}{2233} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 660x+275x& = & 30-132 \\\Leftrightarrow & \color{red}{935} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{935} & & \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{3})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{10}{3}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{+10} & = & \color{red}{15x} +8 \\\Leftrightarrow & 18x \color{red}{+10} \color{blue}{-10} \color{blue}{-15x} & = & \color{red}{15x} +8 \color{blue}{-15x} \color{blue}{-10} \\\Leftrightarrow & 18x-15x& = & 8-10 \\\Leftrightarrow & \color{red}{3} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{-20} & = & \color{red}{-9x} +10 \\\Leftrightarrow & 60x \color{red}{-20} \color{blue}{+20} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{+20} \\\Leftrightarrow & 60x+9x& = & 10+20 \\\Leftrightarrow & \color{red}{69} x& = & 30 \\\Leftrightarrow & x = \frac{30}{69} & & \\\Leftrightarrow & x = \frac{10}{23} & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{175x} +20 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 420x-175x& = & 20+84 \\\Leftrightarrow & \color{red}{245} x& = & 104 \\\Leftrightarrow & x = \frac{104}{245} & & \\ & V = \left\{ \frac{104}{245} \right\} & \\\end{align}\)