Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{7})& = & 2x+\frac{8}{5} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 2x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-30} & = & \color{red}{70x} +56 \\\Leftrightarrow & 315x \color{red}{-30} \color{blue}{+30} \color{blue}{-70x} & = & \color{red}{70x} +56 \color{blue}{-70x} \color{blue}{+30} \\\Leftrightarrow & 315x-70x& = & 56+30 \\\Leftrightarrow & \color{red}{245} x& = & 86 \\\Leftrightarrow & x = \frac{86}{245} & & \\ & V = \left\{ \frac{86}{245} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -4x+\frac{3}{4} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -4x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{-40} & = & \color{red}{-112x} +21 \\\Leftrightarrow & -420x \color{red}{-40} \color{blue}{+40} \color{blue}{+112x} & = & \color{red}{-112x} +21 \color{blue}{+112x} \color{blue}{+40} \\\Leftrightarrow & -420x+112x& = & 21+40 \\\Leftrightarrow & \color{red}{-308} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-308} & & \\\Leftrightarrow & x = \frac{-61}{308} & & \\ & V = \left\{ \frac{-61}{308} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+72} & = & \color{red}{-165x} +55 \\\Leftrightarrow & 396x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +55 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & 396x+165x& = & 55-72 \\\Leftrightarrow & \color{red}{561} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{561} & & \\\Leftrightarrow & x = \frac{-1}{33} & & \\ & V = \left\{ \frac{-1}{33} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{105x} +10 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 135x-105x& = & 10-36 \\\Leftrightarrow & \color{red}{30} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{30} & & \\\Leftrightarrow & x = \frac{-13}{15} & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 150x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & 150x+35x& = & 6+12 \\\Leftrightarrow & \color{red}{185} x& = & 18 \\\Leftrightarrow & x = \frac{18}{185} & & \\ & V = \left\{ \frac{18}{185} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{11})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-70} & = & \color{red}{231x} +110 \\\Leftrightarrow & 616x \color{red}{-70} \color{blue}{+70} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+70} \\\Leftrightarrow & 616x-231x& = & 110+70 \\\Leftrightarrow & \color{red}{385} x& = & 180 \\\Leftrightarrow & x = \frac{180}{385} & & \\\Leftrightarrow & x = \frac{36}{77} & & \\ & V = \left\{ \frac{36}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{11})& = & -7x+\frac{7}{11} \\\Leftrightarrow & 20x+\frac{12}{11}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+12} & = & \color{red}{-77x} +7 \\\Leftrightarrow & 220x \color{red}{+12} \color{blue}{-12} \color{blue}{+77x} & = & \color{red}{-77x} +7 \color{blue}{+77x} \color{blue}{-12} \\\Leftrightarrow & 220x+77x& = & 7-12 \\\Leftrightarrow & \color{red}{297} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{297} & & \\ & V = \left\{ \frac{-5}{297} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{11})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{+120} & = & \color{red}{220x} +55 \\\Leftrightarrow & 792x \color{red}{+120} \color{blue}{-120} \color{blue}{-220x} & = & \color{red}{220x} +55 \color{blue}{-220x} \color{blue}{-120} \\\Leftrightarrow & 792x-220x& = & 55-120 \\\Leftrightarrow & \color{red}{572} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{572} & & \\\Leftrightarrow & x = \frac{-5}{44} & & \\ & V = \left\{ \frac{-5}{44} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 21x-\frac{21}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x- \frac{189}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{-189} & = & \color{red}{-495x} +88 \\\Leftrightarrow & 2079x \color{red}{-189} \color{blue}{+189} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{+189} \\\Leftrightarrow & 2079x+495x& = & 88+189 \\\Leftrightarrow & \color{red}{2574} x& = & 277 \\\Leftrightarrow & x = \frac{277}{2574} & & \\ & V = \left\{ \frac{277}{2574} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -16x-\frac{20}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{-220} & = & \color{red}{-231x} +18 \\\Leftrightarrow & -528x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & -528x+231x& = & 18+220 \\\Leftrightarrow & \color{red}{-297} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-297} & & \\\Leftrightarrow & x = \frac{-238}{297} & & \\ & V = \left\{ \frac{-238}{297} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{3})& = & -3x+\frac{7}{10} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{+200} & = & \color{red}{-90x} +21 \\\Leftrightarrow & -600x \color{red}{+200} \color{blue}{-200} \color{blue}{+90x} & = & \color{red}{-90x} +21 \color{blue}{+90x} \color{blue}{-200} \\\Leftrightarrow & -600x+90x& = & 21-200 \\\Leftrightarrow & \color{red}{-510} x& = & -179 \\\Leftrightarrow & x = \frac{-179}{-510} & & \\\Leftrightarrow & x = \frac{179}{510} & & \\ & V = \left\{ \frac{179}{510} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{-10} & = & \color{red}{33x} +6 \\\Leftrightarrow & 44x \color{red}{-10} \color{blue}{+10} \color{blue}{-33x} & = & \color{red}{33x} +6 \color{blue}{-33x} \color{blue}{+10} \\\Leftrightarrow & 44x-33x& = & 6+10 \\\Leftrightarrow & \color{red}{11} x& = & 16 \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)