Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{7})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 9x+\frac{9}{7}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+45} & = & \color{red}{245x} +56 \\\Leftrightarrow & 315x \color{red}{+45} \color{blue}{-45} \color{blue}{-245x} & = & \color{red}{245x} +56 \color{blue}{-245x} \color{blue}{-45} \\\Leftrightarrow & 315x-245x& = & 56-45 \\\Leftrightarrow & \color{red}{70} x& = & 11 \\\Leftrightarrow & x = \frac{11}{70} & & \\ & V = \left\{ \frac{11}{70} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{14}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{-140x} +14 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +14 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -120x+140x& = & 14+75 \\\Leftrightarrow & \color{red}{20} x& = & 89 \\\Leftrightarrow & x = \frac{89}{20} & & \\ & V = \left\{ \frac{89}{20} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -2x+\frac{10}{11} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -2x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{+154} & = & \color{red}{-66x} +30 \\\Leftrightarrow & 693x \color{red}{+154} \color{blue}{-154} \color{blue}{+66x} & = & \color{red}{-66x} +30 \color{blue}{+66x} \color{blue}{-154} \\\Leftrightarrow & 693x+66x& = & 30-154 \\\Leftrightarrow & \color{red}{759} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{759} & & \\ & V = \left\{ \frac{-124}{759} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-84} & = & \color{red}{-245x} +45 \\\Leftrightarrow & -840x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +45 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & -840x+245x& = & 45+84 \\\Leftrightarrow & \color{red}{-595} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-595} & & \\\Leftrightarrow & x = \frac{-129}{595} & & \\ & V = \left\{ \frac{-129}{595} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{4})& = & -4x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{25}{4}& = & -4x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x- \frac{125}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{-125} & = & \color{red}{-80x} +32 \\\Leftrightarrow & -300x \color{red}{-125} \color{blue}{+125} \color{blue}{+80x} & = & \color{red}{-80x} +32 \color{blue}{+80x} \color{blue}{+125} \\\Leftrightarrow & -300x+80x& = & 32+125 \\\Leftrightarrow & \color{red}{-220} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-220} & & \\\Leftrightarrow & x = \frac{-157}{220} & & \\ & V = \left\{ \frac{-157}{220} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-150} & = & \color{red}{-245x} +14 \\\Leftrightarrow & -1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & -1050x+245x& = & 14+150 \\\Leftrightarrow & \color{red}{-805} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-805} & & \\\Leftrightarrow & x = \frac{-164}{805} & & \\ & V = \left\{ \frac{-164}{805} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{11})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 6x+\frac{15}{11}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+15} & = & \color{red}{-55x} +7 \\\Leftrightarrow & 66x \color{red}{+15} \color{blue}{-15} \color{blue}{+55x} & = & \color{red}{-55x} +7 \color{blue}{+55x} \color{blue}{-15} \\\Leftrightarrow & 66x+55x& = & 7-15 \\\Leftrightarrow & \color{red}{121} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{121} & & \\ & V = \left\{ \frac{-8}{121} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+160} & = & \color{red}{-120x} +21 \\\Leftrightarrow & 288x \color{red}{+160} \color{blue}{-160} \color{blue}{+120x} & = & \color{red}{-120x} +21 \color{blue}{+120x} \color{blue}{-160} \\\Leftrightarrow & 288x+120x& = & 21-160 \\\Leftrightarrow & \color{red}{408} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{408} & & \\ & V = \left\{ \frac{-139}{408} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{10})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 9x-\frac{9}{10}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-9} & = & \color{red}{20x} +12 \\\Leftrightarrow & 90x \color{red}{-9} \color{blue}{+9} \color{blue}{-20x} & = & \color{red}{20x} +12 \color{blue}{-20x} \color{blue}{+9} \\\Leftrightarrow & 90x-20x& = & 12+9 \\\Leftrightarrow & \color{red}{70} x& = & 21 \\\Leftrightarrow & x = \frac{21}{70} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+264} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 660x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & 660x+275x& = & 20-264 \\\Leftrightarrow & \color{red}{935} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{935} & & \\ & V = \left\{ \frac{-244}{935} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{7})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 6x-\frac{15}{7}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-165} & = & \color{red}{385x} +21 \\\Leftrightarrow & 462x \color{red}{-165} \color{blue}{+165} \color{blue}{-385x} & = & \color{red}{385x} +21 \color{blue}{-385x} \color{blue}{+165} \\\Leftrightarrow & 462x-385x& = & 21+165 \\\Leftrightarrow & \color{red}{77} x& = & 186 \\\Leftrightarrow & x = \frac{186}{77} & & \\ & V = \left\{ \frac{186}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+1)& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x-5& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{50}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-50} & = & \color{red}{70x} +9 \\\Leftrightarrow & -100x \color{red}{-50} \color{blue}{+50} \color{blue}{-70x} & = & \color{red}{70x} +9 \color{blue}{-70x} \color{blue}{+50} \\\Leftrightarrow & -100x-70x& = & 9+50 \\\Leftrightarrow & \color{red}{-170} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-170} & & \\\Leftrightarrow & x = \frac{-59}{170} & & \\ & V = \left\{ \frac{-59}{170} \right\} & \\\end{align}\)