Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{4}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+12} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 90x \color{red}{+12} \color{blue}{-12} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-12} \\\Leftrightarrow & 90x+75x& = & 40-12 \\\Leftrightarrow & \color{red}{165} x& = & 28 \\\Leftrightarrow & x = \frac{28}{165} & & \\ & V = \left\{ \frac{28}{165} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{4}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-4} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -30x \color{red}{-4} \color{blue}{+4} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{+4} \\\Leftrightarrow & -30x+21x& = & 10+4 \\\Leftrightarrow & \color{red}{-9} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-9} & & \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-132} & = & \color{red}{495x} +30 \\\Leftrightarrow & 440x \color{red}{-132} \color{blue}{+132} \color{blue}{-495x} & = & \color{red}{495x} +30 \color{blue}{-495x} \color{blue}{+132} \\\Leftrightarrow & 440x-495x& = & 30+132 \\\Leftrightarrow & \color{red}{-55} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-55} & & \\\Leftrightarrow & x = \frac{-162}{55} & & \\ & V = \left\{ \frac{-162}{55} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{3})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -16x+\frac{20}{3}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-192}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -192x \color{red}{+80} & = & \color{red}{84x} +15 \\\Leftrightarrow & -192x \color{red}{+80} \color{blue}{-80} \color{blue}{-84x} & = & \color{red}{84x} +15 \color{blue}{-84x} \color{blue}{-80} \\\Leftrightarrow & -192x-84x& = & 15-80 \\\Leftrightarrow & \color{red}{-276} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-276} & & \\\Leftrightarrow & x = \frac{65}{276} & & \\ & V = \left\{ \frac{65}{276} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-36} & = & \color{red}{-120x} +40 \\\Leftrightarrow & -225x \color{red}{-36} \color{blue}{+36} \color{blue}{+120x} & = & \color{red}{-120x} +40 \color{blue}{+120x} \color{blue}{+36} \\\Leftrightarrow & -225x+120x& = & 40+36 \\\Leftrightarrow & \color{red}{-105} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-105} & & \\\Leftrightarrow & x = \frac{-76}{105} & & \\ & V = \left\{ \frac{-76}{105} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{+12} & = & \color{red}{35x} +6 \\\Leftrightarrow & -80x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & -80x-35x& = & 6-12 \\\Leftrightarrow & \color{red}{-115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-115} & & \\\Leftrightarrow & x = \frac{6}{115} & & \\ & V = \left\{ \frac{6}{115} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -30x+\frac{18}{5}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+126} & = & \color{red}{245x} +10 \\\Leftrightarrow & -1050x \color{red}{+126} \color{blue}{-126} \color{blue}{-245x} & = & \color{red}{245x} +10 \color{blue}{-245x} \color{blue}{-126} \\\Leftrightarrow & -1050x-245x& = & 10-126 \\\Leftrightarrow & \color{red}{-1295} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{-1295} & & \\\Leftrightarrow & x = \frac{116}{1295} & & \\ & V = \left\{ \frac{116}{1295} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{20}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+140} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 924x \color{red}{+140} \color{blue}{-140} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-140} \\\Leftrightarrow & 924x+385x& = & 110-140 \\\Leftrightarrow & \color{red}{1309} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{1309} & & \\ & V = \left\{ \frac{-30}{1309} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & 3x+\frac{5}{4} \\\Leftrightarrow & 20x+\frac{20}{11}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{880}{ \color{blue}{44} }x+ \frac{80}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 880x \color{red}{+80} & = & \color{red}{132x} +55 \\\Leftrightarrow & 880x \color{red}{+80} \color{blue}{-80} \color{blue}{-132x} & = & \color{red}{132x} +55 \color{blue}{-132x} \color{blue}{-80} \\\Leftrightarrow & 880x-132x& = & 55-80 \\\Leftrightarrow & \color{red}{748} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{748} & & \\ & V = \left\{ \frac{-25}{748} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{9})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 8x+\frac{20}{9}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+20} & = & \color{red}{-63x} +4 \\\Leftrightarrow & 72x \color{red}{+20} \color{blue}{-20} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{-20} \\\Leftrightarrow & 72x+63x& = & 4-20 \\\Leftrightarrow & \color{red}{135} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{135} & & \\ & V = \left\{ \frac{-16}{135} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-168} & = & \color{red}{315x} +40 \\\Leftrightarrow & -630x \color{red}{-168} \color{blue}{+168} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+168} \\\Leftrightarrow & -630x-315x& = & 40+168 \\\Leftrightarrow & \color{red}{-945} x& = & 208 \\\Leftrightarrow & x = \frac{208}{-945} & & \\\Leftrightarrow & x = \frac{-208}{945} & & \\ & V = \left\{ \frac{-208}{945} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{18}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{-54} & = & \color{red}{105x} +50 \\\Leftrightarrow & 450x \color{red}{-54} \color{blue}{+54} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{+54} \\\Leftrightarrow & 450x-105x& = & 50+54 \\\Leftrightarrow & \color{red}{345} x& = & 104 \\\Leftrightarrow & x = \frac{104}{345} & & \\ & V = \left\{ \frac{104}{345} \right\} & \\\end{align}\)